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%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Javier Martinez at 2020-10-26 15:48:20 +0100
%% Saved with string encoding Unicode (UTF-8)
@comment{jabref-meta: databaseType:bibtex;}
@preprint{hurri2023,
title= {On the Weighted Inequality Between the Gagliardo and Sobolev Seminorms},
author={Hurri-Syrj{\"a}nen, Ritva and Mart\'inez-Perales, Javier and P\'erez, Carlos and V{\"a}h{\"a}kangas, Antti},
journal={Preprint},
year={2023}
}
@article{martinez2023,
title={Remarks on vector-valued Gagliardo and Poincar\'e-Sobolev type inequalities with weights},
author={Mart\'inez-Perales, Javier and P\'erez, Carlos},
journal={Potentials and Partial Differential Equations. The Legacy of David R. Adams},
year={2023}
}
@article{martinez2020quantitative,
year = {2022},
title = {{Quantitative John–Nirenberg inequalities at different scales}},
author = {Mart\'inez-Perales, Javier C. and Rela, Ezequiel and Rivera-R\'ios, Israel P},
journal = {Revista Matemática Complutense},
issn = {1139-1138},
doi = {10.1007/s13163-022-00427-0},
abstract = {},
pages = {1--35}
}
@article{kosz2022maximal,
title={Maximal operators on the infinite-dimensional torus},
author={Kosz, Dariusz and Mart{\'\i}nez-Perales, Javier C and Paternostro, Victoria and Rela, Ezequiel and Roncal, Luz},
journal={\href{https://rdcu.be/cKk2Y}{Mathematische Annalen}},
pages={1--39},
year={2022},
publisher={Springer Berlin Heidelberg}
}
@article{hurri2022bbm,
title={On the BBM-phenomenon in fractional Poincare-Sobolev inequalities with weights},
author={Hurri-Syrj{\"a}nen, Ritva and Mart\'inez-Perales, Javier and P\'erez, Carlos and V{\"a}h{\"a}kangas, Antti},
journal = {International Mathematics Research Notices},
year = {2022},
month = {09},
issn = {1073-7928},
doi = {10.1093/imrn/rnac246},
url = {https://doi.org/10.1093/imrn/rnac246},
note = {rnac246}
}
@misc{HMPV2022,
title={Degenerate fractional Poincar\'e-Sobolev inequalities with double extra gain},
author={Ritva Hurri-Syrj\"anen and Javier C. Mart\'inez-Perales and Carlos P\'erez and Antti V. V\"ah\"akangas},
year={2022},
eprint={2201.11712},
archivePrefix={arXiv},
primaryClass={math.CA}
}
@misc{Kosz2021,
title={Maximal operators on the infinite-dimensional torus},
author={Darius Kosz and Javier Mart\'inez Perales and Victoria Paternostro and Ezequiel Rela and Luz Roncal},
year={2021},
eprint={2109.04811},
archivePrefix={arXiv},
primaryClass={math.CA}
}
@article{Christ1990,
Author = {Christ, Michael},
Date-Added = {2020-10-26 14:34:24 +0100},
Date-Modified = {2020-10-26 14:34:56 +0100},
Journal = {Colloquium Mathematicum},
Pages = {601-628},
Title = {A $T(b)$ theorem with remarks on analytic capacity and the Cauchy integral},
Volume = {60},
Year = {1990}}
@article{Franchi2000,
Author = {Franchi, Bruno and Haj\l{}asz, Piotr},
Date-Added = {2020-10-26 12:21:26 +0100},
Date-Modified = {2020-10-26 12:22:51 +0100},
Journal = {Annales Polonici Mathematici},
Pages = {97-103},
Title = {How to get rid of one of the weights in a two-weight Poincar\'e inequality?},
Volume = {74},
Year = {2000}}
@article{Brezis2002,
Abstract = {A criterion for a function f ∈ Lp to belong to W1,p (p > 1) or to BV (p = 1) is given. Various integral conditions under which a measurable function is constant are discussed.},
Author = {Ha\"im Br\'ezis},
Date-Added = {2020-09-20 17:37:35 +0200},
Date-Modified = {2020-09-20 17:37:50 +0200},
Day = {1},
Doi = {http://sci-hub.tw/10.1070/RM2002v057n04ABEH000533},
Issn = {0036-0279},
Journal = {Russian Mathematical Surveys},
Language = {English (US)},
Month = jul,
Number = {4},
Pages = {693--708},
Publisher = {IOP Publishing Ltd.},
Title = {How to recognize constant functions. Connections with Sobolev spaces},
Volume = {57},
Year = {2002},
Bdsk-Url-1 = {http://sci-hub.tw/10.1070/RM2002v057n04ABEH000533}}
@book{Mazya1985,
Author = {Maz'ya, Vladimir},
Date-Added = {2020-09-20 12:49:10 +0200},
Date-Modified = {2020-09-20 12:50:22 +0200},
Edition = {1},
Publisher = {Springer-Verlag Berlin Heidelberg},
Title = {Sobolev Spaces},
Year = {1985}}
@article{Kolyada2005,
Author = {Kolyada, Viktor and Lerner, Andrei},
Date-Added = {2020-09-19 11:29:24 +0200},
Date-Modified = {2020-09-19 11:29:52 +0200},
Doi = {10.4064/sm171-1-1},
Journal = {Studia Math.},
Month = {01},
Title = {On limiting embeddings of Besov spaces},
Volume = {171},
Year = {2005},
Bdsk-Url-1 = {https://doi.org/10.4064/sm171-1-1}}
@phdthesis{Shanmugalingam1999,
Author = {Shanmugalingam, Nageswari},
Date-Added = {2020-09-18 20:35:27 +0200},
Date-Modified = {2020-09-18 20:36:13 +0200},
School = {University of Michigan},
Title = {Newtonian spaces: an extension of Sobolev spaces to metric measure spaces},
Year = {1999}}
@article{Shanmugalingam2000,
Abstract = {This paper studies a possible definition of Sobolev spaces in abstract metric spaces, and answers in the affirmative the question whether this definition yields a Banach space. The paper also explores the relationship between this definition and the Hajlasz spaces. For specialized metric spaces the Sobolev embedding theorems are proven. Different versions of capacities are also explored, and these various definitions are compared. The main tool used in this paper is the concept of moduli of path families.},
Author = {Shanmugalingam, Nageswari},
Date-Added = {2020-09-18 20:34:42 +0200},
Date-Modified = {2020-09-18 20:34:42 +0200},
Journal = {Revista Matem{\'a}tica Iberoamericana},
Keywords = {Espacios de Sobolev; Espacios de Banach; Sobolev space; metric measure space; doubling space; gradient; Poincar{\'e} inequality; embedding theorem; capacity; path family},
Language = {eng},
Number = {2},
Pages = {243-279},
Title = {Newtonian spaces: An extension of Sobolev spaces to metric measure spaces.},
Url = {http://eudml.org/doc/39609},
Volume = {16},
Year = {2000},
Bdsk-Url-1 = {http://eudml.org/doc/39609}}
@article{Heinonen1998,
Author = {Heinonen, Juha and Koskela, Pekka},
Date-Added = {2020-09-18 20:18:31 +0200},
Date-Modified = {2020-09-18 20:18:58 +0200},
Doi = {10.1007/BF02392747},
Fjournal = {Acta Mathematica},
Journal = {Acta Math.},
Number = {1},
Pages = {1--61},
Publisher = {Institut Mittag-Leffler},
Title = {Quasiconformal maps in metric spaces with controlled geometry},
Url = {https://doi.org/10.1007/BF02392747},
Volume = {181},
Year = {1998},
Bdsk-Url-1 = {https://doi.org/10.1007/BF02392747}}
@misc{Luda2019,
Archiveprefix = {arXiv},
Author = {Korobenko, Lyudmila},
Date-Added = {2020-07-11 17:43:44 +0200},
Date-Modified = {2020-07-11 17:44:15 +0200},
Eprint = {1906.04088},
Primaryclass = {math.AP},
Title = {Orlicz Sobolev Inequalities and the Doubling Condition},
Year = {2019},
Bdsk-File-1 = {YnBsaXN0MDDSAQIDBFxyZWxhdGl2ZVBhdGhZYWxpYXNEYXRhXxAZUmVmZXJlbmNpYXMvQ2FudG8yMDE5LnBkZk8RAWoAAAAAAWoAAgAAAkhEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABCRAAB/////w1DYW50bzIwMTkucGRmAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD/////AAAAAAAAAAAAAAAAAAEAAwAACiBjdQAAAAAAAAAAAAAAAAALUmVmZXJlbmNpYXMAAAIAQS86VXNlcnM6am1hcnRpbmV6OkRyb3Bib3g6VmVyYlRlWDpUZXNpczpSZWZlcmVuY2lhczpDYW50bzIwMTkucGRmAAAOABwADQBDAGEAbgB0AG8AMgAwADEAOQAuAHAAZABmAA8ABgACAEgARAASAD9Vc2Vycy9qbWFydGluZXovRHJvcGJveC9WZXJiVGVYL1Rlc2lzL1JlZmVyZW5jaWFzL0NhbnRvMjAxOS5wZGYAABMAAS8AABUAAgAQ//8AAAAIAA0AGgAkAEAAAAAAAAACAQAAAAAAAAAFAAAAAAAAAAAAAAAAAAABrg==}}
@misc{Kosz2020,
Archiveprefix = {arXiv},
Author = {Kosz, Dariusz},
Date-Added = {2020-07-11 17:39:35 +0200},
Date-Modified = {2020-07-11 17:40:15 +0200},
Eprint = {2003.01633},
Primaryclass = {math.CA},
Title = {On differentiation of integrals in the infinite-dimensional torus},
Year = {2019},
Bdsk-File-1 = {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}}
@misc{Hytoenen2018,
Archiveprefix = {arXiv},
Author = {Hyt\"onen, Tuomas P.},
Date-Added = {2020-07-11 17:33:25 +0200},
Date-Modified = {2020-07-11 17:34:12 +0200},
Eprint = {1804.11167},
Primaryclass = {math.CA},
Title = {The $L^p$-to-$L^q$ boundedness of commutators with applications to the Jacobian operator},
Year = {2018},
Bdsk-File-1 = {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}}
@article{Azzam2019,
Author = {Azzam, Jonas and Hofmann, Steve and Martell, Jos\'e Mar\'ia and Mourgoglou, Mihalis and Tolsa, Xavier},
Doi = {https://doi.org/10.1007/s00222-020-00984-5},
Journal = {Invent. Math.},
Title = {Harmonic measure and quantitative connectivity: geometric characterization of the $L^p$ solvability of the Dirichlet problem},
Year = {2020},
Bdsk-File-1 = {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}}
@book{villani2016,
Author = {Villani, C\'edric},
Date-Added = {2020-06-16 10:13:05 +0200},
Date-Modified = {2020-07-10 12:36:43 +0200},
Isbn = {9783662501801},
Publisher = {Springer Berlin Heidelberg},
Series = {Grundlehren der mathematischen Wissenschaften},
Title = {Optimal Transport: Old and New},
Url = {https://books.google.es/books?id=5p8SDAEACAAJ},
Year = {2016},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {https://books.google.es/books?id=5p8SDAEACAAJ}}
@article{Ho2014,
Author = {Ho, Kwok-Pun},
Date-Added = {2020-05-27 10:59:09 +0200},
Date-Modified = {2020-05-27 10:59:58 +0200},
Doi = {10.11650/tjm.18.2014.3618},
Fjournal = {Taiwanese Journal of Mathematics},
Journal = {Taiwanese J. Math.},
Month = {08},
Number = {4},
Pages = {1107--1118},
Publisher = {Mathematical Society of the Republic of China},
Title = {John-Nirenberg inequalities on Lebesgue spaces with variable exponents},
Url = {https://doi.org/10.11650/tjm.18.2014.3618},
Volume = {18},
Year = {2014},
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Bdsk-Url-1 = {https://doi.org/10.11650/tjm.18.2014.3618}}
@book{Cruz-Uribe2013-2,
Author = {Cruz-Uribe, David and Fiorenza, Alberto},
Date-Added = {2020-05-25 17:27:36 +0200},
Date-Modified = {2020-05-25 17:35:23 +0200},
Publisher = {Birkhauser},
Series = {Applied and Numerical Harmonic Analysis},
Title = {Variable Lebesgue Spaces: Foundations and Harmonic Analysis},
Year = {2013},
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@article{Cianchi1996-2,
Abstract = {We associate with any Young function A a Young function B having the property that, for any sufficiently smooth subset G of Rn, LB(G) is the smallest Orlicz space into which the Orlicz-Sobolev space W1,A(G) is continuously embedded.},
Author = {Andrea Cianchi},
Date-Added = {2020-05-22 19:57:55 +0200},
Date-Modified = {2020-07-11 17:05:33 +0200},
Issn = {00222518, 19435258},
Journal = {Indiana U. Math. J.},
Number = {1},
Pages = {39--65},
Publisher = {Indiana University Mathematics Department},
Title = {A Sharp Embedding Theorem for Orlicz-Sobolev Spaces},
Url = {http://www.jstor.org/stable/24899146},
Volume = {45},
Year = {1996},
Bdsk-Url-1 = {http://www.jstor.org/stable/24899146}}
@article{Cianchi1996,
Author = {Cianchi, Andrea},
Date-Added = {2020-05-22 19:56:28 +0200},
Date-Modified = {2020-07-11 17:05:12 +0200},
Journal = {Ann. Scuola. Norm.-Sci.},
Language = {en},
Mrnumber = {1440034},
Number = {3},
Pages = {575-608},
Publisher = {Scuola normale superiore},
Title = {Continuity properties of functions from Orlicz-Sobolev spaces and embedding theorems},
Url = {http://www.numdam.org/item/ASNSP_1996_4_23_3_575_0},
Volume = {Ser. 4, 23},
Year = {1996},
Zbl = {0877.46023},
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Bdsk-Url-1 = {http://www.numdam.org/item/ASNSP_1996_4_23_3_575_0}}
@article{MacManus2002,
Author = {MacManus, Paul and P{\'e}rez, Carlos},
Date-Added = {2020-05-22 19:55:19 +0200},
Date-Modified = {2020-07-11 17:45:09 +0200},
Journal = {Trans. Amer. Math. Soc.},
Number = {5},
Pages = {1997--2012},
Title = {Trudinger inequalities without derivatives},
Volume = {354},
Year = {2002},
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@article{Caruso2001,
Author = {Caruso, Andrea},
Date-Added = {2020-05-22 17:47:55 +0200},
Date-Modified = {2020-07-11 17:02:23 +0200},
Journal = {Matematiche (Catania)},
Number = {1},
Pages = {183--194},
Title = {Two properties of norms in Orlicz spaces},
Volume = {56},
Year = {2001},
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@phdthesis{TesisHeikkinen,
Author = {Heikkinen, Toni},
Date-Added = {2020-05-22 17:37:42 +0200},
Date-Modified = {2020-05-22 17:38:05 +0200},
Title = {Self-improving properties of generalized Orlicz-Poincar\'e inequalities},
Year = {2006},
Bdsk-File-1 = {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}}
@book{Krasnoselskii1961,
Author = {Krasnosel'skii, Mark Alexandrovich and Rutickii, Yakov Bronislavovich},
Date-Added = {2020-05-22 13:43:39 +0200},
Date-Modified = {2020-10-02 12:23:01 +0200},
Publisher = {Noordhoff, Groningen, The Netherlands},
Title = {Convex Functions and Orlicz Spaces},
Year = {1961},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {https://doi.org/10.2307/3613435}}
@article{Karagulyan2002,
Abstract = {In this paper we study the properties of the maximal operator generated by the Calder{\'o}n--Zygmund operator. In particular, we refine Hunt's inequality.},
Author = {Karagulyan, Grigori A.},
Da = {2002/03/01},
Date-Added = {2020-05-18 20:14:19 +0200},
Date-Modified = {2020-07-11 17:37:57 +0200},
Doi = {10.1023/A:1014850924850},
Id = {Karagulyan2002},
Isbn = {1573-8876},
Journal = {Math. Notes},
Number = {3},
Pages = {362--373},
Title = {Exponential Estimates of the Calder\'on--Zygmund Operator and Related Questions about Fourier Series},
Ty = {JOUR},
Url = {https://doi.org/10.1023/A:1014850924850},
Volume = {71},
Year = {2002},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {https://doi.org/10.1023/A:1014850924850}}
@article{Hajlasz1998,
Abstract = {The paper proves several weighted imbedding theorems for domains with fractal boundaries. The weights considered are distances to the boundary to certain powers, and the domains are so-called s-John domains. The paper also proves, in the general setting, that the existence of an imbedding implies compactness of the imbedding for lower exponents. Moreover, following Maz'ya, the paper reformulates the imbedding theorems in the language of local isoperimetric and capacity estimates.},
Author = {Haj\l{}asz, Piotrasz, Piotr and Koskela, Pekka},
Date-Added = {2020-05-15 18:09:21 +0200},
Date-Modified = {2020-07-11 17:23:48 +0200},
Doi = {10.1112/S0024610798006346},
Eprint = {https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/S0024610798006346},
Journal = {J. Lond. Math. Soc.},
Number = {2},
Pages = {425-450},
Title = {Isoperimetric Inequalities and Imbedding Theorems in Irregular Domains},
Url = {https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0024610798006346},
Volume = {58},
Year = {1998},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0024610798006346},
Bdsk-Url-2 = {https://doi.org/10.1112/S0024610798006346}}
@article{Mazya1964,
Author = {Maz'ya, Vladimir},
Date-Added = {2020-05-15 18:05:34 +0200},
Date-Modified = {2020-05-15 18:07:04 +0200},
Journal = {Akad. Nauk.},
Pages = {1145--1172},
Title = {A theorem on the multidimensional Schr\"odinger operator},
Volume = {28},
Year = {1964}}
@article{Burkholder1970,
Author = {Burkholder, Donald Lyman and Gundy, Richard F.},
Date-Added = {2020-05-14 18:20:31 +0200},
Date-Modified = {2020-07-10 11:57:49 +0200},
Doi = {10.1007/BF02394573},
Fjournal = {Acta Mathematica},
Journal = {Acta Math.},
Pages = {249--304},
Publisher = {Institut Mittag-Leffler},
Title = {Extrapolation and interpolation of quasi-linear operators on martingales},
Url = {https://doi.org/10.1007/BF02394573},
Volume = {124},
Year = {1970},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {https://doi.org/10.1007/BF02394573}}
@book{Zaanen1967,
Author = {Zaanen, Adriaan C.},
Date-Added = {2020-05-13 22:08:40 +0200},
Date-Modified = {2020-07-10 12:39:11 +0200},
Edition = {2nd rev. ed.},
Publisher = {North Holland, Amsterdam; Interscience, New York},
Title = {Integration},
Year = {1967}}
@book{Okada2008,
Author = {Okada, Susumu and Ricker, Wener J. and S\'anchez P\'erez, Enrique A.},
Date-Added = {2020-05-13 19:57:49 +0200},
Date-Modified = {2020-05-13 20:05:00 +0200},
Publisher = {Birkh\"auser Basel},
Series = {Operator Theory: Advances and Applications},
Title = {Optimal Domain and Integral Extension of Operators},
Volume = {180},
Year = {2008},
Bdsk-File-1 = {YnBsaXN0MDDSAQIDBFxyZWxhdGl2ZVBhdGhZYWxpYXNEYXRhXxAZUmVmZXJlbmNpYXMvT2thZGEyMDA4LnBkZk8RAWoAAAAAAWoAAgAAAkhEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABCRAAB/////w1Pa2FkYTIwMDgucGRmAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD/////AAAAAAAAAAAAAAAAAAEAAwAACiBjdQAAAAAAAAAAAAAAAAALUmVmZXJlbmNpYXMAAAIAQS86VXNlcnM6am1hcnRpbmV6OkRyb3Bib3g6VmVyYlRlWDpUZXNpczpSZWZlcmVuY2lhczpPa2FkYTIwMDgucGRmAAAOABwADQBPAGsAYQBkAGEAMgAwADAAOAAuAHAAZABmAA8ABgACAEgARAASAD9Vc2Vycy9qbWFydGluZXovRHJvcGJveC9WZXJiVGVYL1Rlc2lzL1JlZmVyZW5jaWFzL09rYWRhMjAwOC5wZGYAABMAAS8AABUAAgAQ//8AAAAIAA0AGgAkAEAAAAAAAAACAQAAAAAAAAAFAAAAAAAAAAAAAAAAAAABrg==}}
@incollection{Garofalo2019,
Author = {Garofalo, Nicola},
Booktitle = {New developments in the analysis of nonlocal operators},
Date-Added = {2020-05-12 16:14:03 +0200},
Date-Modified = {2020-05-12 16:14:11 +0200},
Doi = {10.1090/conm/723/14569},
Mrclass = {35R11 (35S05)},
Mrnumber = {3916700},
Mrreviewer = {Vincenzo Ambrosio},
Pages = {1--135},
Publisher = {Amer. Math. Soc., Providence, RI},
Series = {Contemp. Math.},
Title = {Fractional thoughts},
Url = {https://doi.org/10.1090/conm/723/14569},
Volume = {723},
Year = {2019},
Bdsk-Url-1 = {https://doi.org/10.1090/conm/723/14569}}
@article{TEMAT,
Author = {Accomazzo Scotti, Natalia and Baena Miret, Sergio and Becerra Tom\'e, Alberto and Mart\'inez-Perales, Javier C. and Rodr\'iguez Abella, \'Alvaro and Soler Albaladejo, Isabel},
Date-Added = {2020-05-11 18:29:06 +0200},
Date-Modified = {2020-05-17 22:53:37 +0200},
Journal = {TEMat: monogr\'aficos, 1},
Year = {2020},
Pages = {47--60},
Title = {Four different approaches to the fractional Laplacian}}
@article{TEMAT2,
Author = {Mart\'inez-Perales, Javier C.},
Journal = {TEMat, 1},
Year = {2017},
Pages = {15--23},
Title = {La integral de Henstock-Kurzweil y el segundo teorema fundamental del c\'alculo}}
@book{Petersen1977,
Author = {Petersen, Karl E.},
Date-Added = {2020-05-11 17:14:27 +0200},
Date-Modified = {2020-07-10 12:33:34 +0200},
Isbn = {9780521215121},
Lccn = {lc76046860},
Publisher = {Cambridge University Press},
Series = {London Mathematical Society lecture note series and Cassels, J.W.S.},
Title = {Brownian Motion, Hardy Spaces and Bounded Mean Oscillation},
Url = {https://books.google.es/books?id=O2wqDnJ8hFwC},
Year = {1977},
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Bdsk-Url-1 = {https://books.google.es/books?id=O2wqDnJ8hFwC}}
@article{Kolmogorov1925,
Author = {Kolmogorov, Andr\'ei},
Date-Added = {2020-05-08 16:41:22 +0200},
Date-Modified = {2020-07-11 17:38:41 +0200},
Journal = {Fund. Math.},
Pages = {24--29},
Title = {Sur les fonctions harmoniques conjugu\'ees et les s\'eries de Fourier},
Volume = {7},
Year = {1925},
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@article{Coifman1980,
Author = {Coifman, Ronald and Rochberg, Richard},
Date-Added = {2020-05-08 12:22:21 +0200},
Date-Modified = {2020-07-11 17:07:28 +0200},
Doi = {10.2307/2043245},
Journal = {Proc. Amer. Math. Soc.},
Month = {02},
Pages = {249-249},
Title = {Another Characterization of $\mathrm{BMO}$},
Volume = {79},
Year = {1980},
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Bdsk-Url-1 = {https://doi.org/10.2307/2043245}}
@article{Coifman1983,
Author = {Coifman, Ronald and Jones, Peter and Rubio de Francia, Jos\'e},
Date-Added = {2020-05-07 20:21:55 +0200},
Date-Modified = {2020-07-11 17:07:36 +0200},
Doi = {10.2307/2043357},
Journal = {Proc. Amer. Math. Soc.},
Month = {04},
Title = {Constructive Decomposition of $\mathrm{BMO}$ Functions and Factorization of $A_p$ Weights},
Volume = {87},
Year = {1983},
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Bdsk-Url-1 = {https://doi.org/10.2307/2043357}}
@inproceedings{RubiodeFrancia1982-2,
Address = {Rome},
Author = {Rubio de Francia, Jos\'e L.},
Booktitle = {Topics in modern harmonic analysis},
Date-Added = {2020-05-07 20:20:26 +0200},
Date-Modified = {2020-07-11 17:55:58 +0200},
Organization = {Ist. Naz. Alta Mat. Francesco Severi},
Pages = {571--579},
Title = {A new technique in the theory of $A_p$ weights},
Volume = {I, II},
Year = {1983}}
@article{RubiodeFrancia1984,
Author = {Rubio de Francia, Jos\'e L.},
Date-Added = {2020-05-07 20:15:59 +0200},
Date-Modified = {2020-07-11 17:56:08 +0200},
Issn = {00029327, 10806377},
Journal = {Amer. J. Math.},
Number = {3},
Pages = {533--547},
Publisher = {Johns Hopkins University Press},
Title = {Factorization Theory and $A_p$ Weights},
Url = {http://www.jstor.org/stable/2374284},
Volume = {106},
Year = {1984},
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Bdsk-Url-1 = {http://www.jstor.org/stable/2374284}}
@article{RubiodeFrancia1982,
Author = {Rubio de Francia, Jos\'e L.},
Date-Added = {2020-05-07 20:13:39 +0200},
Date-Modified = {2020-07-10 12:34:42 +0200},
Fjournal = {Bulletin (New Series) of the American Mathematical Society},
Journal = {Bull. Amer. Math. Soc. (N.S.)},
Month = {09},
Number = {2},
Pages = {393--395},
Publisher = {American Mathematical Society},
Title = {Factorization and extrapolation of weights},
Url = {https://projecteuclid.org:443/euclid.bams/1183549644},
Volume = {7},
Year = {1982},
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Bdsk-Url-1 = {https://projecteuclid.org:443/euclid.bams/1183549644}}
@article{GarciaCuerva1987,
Author = {Garc\'ia-Cuerva, Jos\'e},
Date-Added = {2020-05-07 20:02:54 +0200},
Date-Modified = {2020-05-07 20:04:16 +0200},
Journal = {Collect. Math.},
Number = {1},
Pages = {3--15},
Title = {Jos\'e Luis Rubio de Francia},
Volume = {38},
Year = {1987},
Bdsk-File-1 = {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}}
@incollection{Muckenhoupt1974-2,
Author = {Muckenhoupt, Benjamin},
Booktitle = {Linear Operators and Approximation II/Lineare Operatoren und Approximation II},
Date-Added = {2020-05-07 19:57:37 +0200},
Date-Modified = {2020-05-07 19:58:45 +0200},
Pages = {265--283},
Publisher = {Springer},
Title = {Weighted norm inequalities for classical operators},
Year = {1974},
Bdsk-File-1 = {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}}
@article{Jones1980,
Author = {Jones, Peter W.},
Date-Added = {2020-05-07 19:53:26 +0200},
Date-Modified = {2020-07-11 17:37:28 +0200},
Issn = {0003486X},
Journal = {Ann. Math.},
Number = {3},
Pages = {511--530},
Publisher = {Annals of Mathematics},
Title = {Factorization of $A_p$ Weights},
Url = {http://www.jstor.org/stable/1971107},
Volume = {111},
Year = {1980},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://www.jstor.org/stable/1971107}}
@misc{Canto2019,
Archiveprefix = {arXiv},
Author = {Canto, Javier and P\'erez, Carlos},
Date-Added = {2020-05-07 18:23:39 +0200},
Date-Modified = {2020-07-11 16:55:18 +0200},
Eprint = {1910.12957},
Primaryclass = {math.CA},
Title = {Extensions of the John-Nirenberg theorem and applications},
Year = {2019},
Bdsk-File-1 = {YnBsaXN0MDDSAQIDBFxyZWxhdGl2ZVBhdGhZYWxpYXNEYXRhXxAZUmVmZXJlbmNpYXMvQ2FudG8yMDE5LnBkZk8RAWoAAAAAAWoAAgAAAkhEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABCRAAB/////w1DYW50bzIwMTkucGRmAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD/////AAAAAAAAAAAAAAAAAAEAAwAACiBjdQAAAAAAAAAAAAAAAAALUmVmZXJlbmNpYXMAAAIAQS86VXNlcnM6am1hcnRpbmV6OkRyb3Bib3g6VmVyYlRlWDpUZXNpczpSZWZlcmVuY2lhczpDYW50bzIwMTkucGRmAAAOABwADQBDAGEAbgB0AG8AMgAwADEAOQAuAHAAZABmAA8ABgACAEgARAASAD9Vc2Vycy9qbWFydGluZXovRHJvcGJveC9WZXJiVGVYL1Rlc2lzL1JlZmVyZW5jaWFzL0NhbnRvMjAxOS5wZGYAABMAAS8AABUAAgAQ//8AAAAIAA0AGgAkAEAAAAAAAAACAQAAAAAAAAAFAAAAAAAAAAAAAAAAAAABrg==}}
@article{Conde-Alonso2019,
Abstract = {Consider a totally irregular measure {\$}{\$}{$\backslash$}mu {\$}{\$}μin {\$}{\$}{\{}{\{}{$\backslash$}mathbb {\{}R{\}}{\}}{\}}\^{}{\{}n+1{\}}{\$}{\$}Rn+1, that is, the upper density {\$}{\$}{$\backslash$}limsup {\_}{\{}r{$\backslash$}rightarrow 0{\}}{$\backslash$}frac{\{}{$\backslash$}mu (B(x,r)){\}}{\{}(2r)\^{}n{\}}{\$}{\$}lim supr→0μ(B(x,r))(2r)nis positive {\$}{\$}{$\backslash$}mu {\$}{\$}μ-a.e. in {\$}{\$}{\{}{\{}{$\backslash$}mathbb {\{}R{\}}{\}}{\}}\^{}{\{}n+1{\}}{\$}{\$}Rn+1, and the lower density {\$}{\$}{$\backslash$}liminf {\_}{\{}r{$\backslash$}rightarrow 0{\}}{$\backslash$}frac{\{}{$\backslash$}mu (B(x,r)){\}}{\{}(2r)\^{}n{\}}{\$}{\$}lim infr→0μ(B(x,r))(2r)nvanishes {\$}{\$}{$\backslash$}mu {\$}{\$}μ-a.e. in {\$}{\$}{\{}{\{}{$\backslash$}mathbb {\{}R{\}}{\}}{\}}\^{}{\{}n+1{\}}{\$}{\$}Rn+1. We show that if {\$}{\$}T{\_}{$\backslash$}mu f(x)={$\backslash$}int K(x,y){$\backslash$},f(y){$\backslash$},d{$\backslash$}mu (y){\$}{\$}Tμf(x)=∫K(x,y)f(y)dμ(y)is an operator whose kernel {\$}{\$}K({$\backslash$}cdot ,{$\backslash$}cdot ){\$}{\$}K(·,·)is the gradient of the fundamental solution for a uniformly elliptic operator in divergence form associated with a matrix with H{\"o}lder continuous coefficients, then {\$}{\$}T{\_}{$\backslash$}mu {\$}{\$}Tμis not bounded in {\$}{\$}L\^{}2({$\backslash$}mu ){\$}{\$}L2(μ). This extends a celebrated result proved previously by Eiderman, Nazarov and Volberg for the n-dimensional Riesz transform.},
Author = {Conde-Alonso, Jos\'e M. and Mourgoglou, Mihalis and Tolsa, Xavier},
Da = {2019/02/01},
Date-Added = {2020-05-06 21:13:09 +0200},
Date-Modified = {2020-07-11 17:07:57 +0200},
Doi = {10.1007/s00208-018-1729-1},
Id = {Conde-Alonso2019},
Isbn = {1432-1807},
Journal = {Math. Ann.},
Number = {1},
Pages = {253--285},
Title = {Failure of $L^2$ boundedness of gradients of single layer potentials for measures with zero low density},
Ty = {JOUR},
Url = {https://doi.org/10.1007/s00208-018-1729-1},
Volume = {373},
Year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1007/s00208-018-1729-1}}
@article{Koch1904,
Author = {{von Koch}, Helge},
Date-Added = {2020-05-06 17:20:22 +0200},
Date-Modified = {2020-07-10 12:26:40 +0200},
Fjournal = {{Arkiv f\"or Matematik, Astronomi och Fysik}},
Issn = {0365-4133},
Journal = {{Ark. Mat. Astron. Fys.}},
Language = {French},
Msc2010 = {26A27 28A80},
Pages = {681--702},
Publisher = {Kungliga Svenska Vetenskapsakademien, Stockholm},
Title = {{Sur une courbe continue sans tangente, obtenue par une construction g\'eom\'etrique \'el\'ementaire.}},
Volume = {1},
Year = {1904},
Zbl = {35.0387.02},
Bdsk-File-1 = {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}}
@article{Azzam2015,
Author = {Azzam, Jonas and Hofmann, Steve and Martell, Jos\'e Mar\'ia and Mayboroda, Svitlana and Mourgoglou, Mihalis and Tolsa, Xavier and Volberg, Alexander},
Date-Added = {2020-05-02 21:16:02 +0200},
Date-Modified = {2020-07-11 16:09:58 +0200},
Doi = {10.1007/s00039-016-0371-x},
Journal = {Geom. Funct. Anal.},
Pages = {703--728},
Title = {Rectifiability of harmonic measure},
Volume = {26},
Year = {2016},
Bdsk-Url-1 = {https://doi.org/10.1007/s00039-016-0371-x}}
@article{RubiodeFrancia1988,
Author = {Rubio de Francia, Jos{\'e} L.},
Date-Added = {2020-05-02 21:08:33 +0200},
Date-Modified = {2020-07-10 12:34:59 +0200},
Journal = {Zubia},
Number = {6},
Pages = {7--30},
Title = {El problema de Dirichlet y la medida arm\'onica},
Url = {https://dialnet.unirioja.es/servlet/articulo?codigo=110209},
Year = {1988},
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@article{RubiodeFrancia1978,
Author = {Rubio de Francia, Jos\'e L.},
Date-Added = {2020-05-01 20:58:22 +0200},
Date-Modified = {2020-07-11 17:53:11 +0200},
Journal = {Comment. Math. Prace Mat.},
Pages = {453--466},
Title = {Nets of subgroups in locally compact groups},
Volume = {20},
Year = {1977/78}}
@book{Astala2008,
Author = {Astala, Kari and Iwaniec, Tadeusz and Martin, Gaven},
Date-Added = {2020-04-29 17:23:06 +0200},
Date-Modified = {2020-07-11 16:09:21 +0200},
Isbn = {9781400830114},
Publisher = {Princeton University Press},
Series = {Princeton Mathematical Series},
Title = {Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane},
Url = {https://books.google.es/books?id=O\_3-otfrBW8C},
Year = {2008},
Bdsk-Url-1 = {https://books.google.es/books?id=O%5C_3-otfrBW8C}}
@article{Wheeden1993,
Abstract = {A new characterization is given for the pairs of weight functions v, w for which the fractional maximal function is a bounded operator from $L^p_v(X)$ to $L_w^q(X)$ when 1 < p < q < ∞ and X is a homogeneous space with a group structure. The case when X is n-dimensional Euclidean space is included.},
Author = {Wheeden, Richard},
Date-Added = {2020-04-23 19:19:16 +0200},
Date-Modified = {2020-07-11 17:57:52 +0200},
Journal = {Stud. Math.},
Keywords = {weighted norm inequalities; fractional maximal function; homogeneous space},
Language = {eng},
Number = {3},
Pages = {257-272},
Title = {A characterization of some weighted norm inequalities for the fractional maximal function},
Url = {http://eudml.org/doc/216032},
Volume = {107},
Year = {1993},
Bdsk-Url-1 = {http://eudml.org/doc/216032}}
@article{Perez1995-2,
Abstract = {We prove endpoint estimates for commutatotrs of singular integrals with BMO functions. We first show that they satisfy L(log L) type inequalities and then that there is a Hardy space type estimate where the usual atomic Hardy space is replaced by an appropriate subspace.},
Author = {P\'erez, Carlos},
Date-Added = {2020-04-15 13:19:18 +0200},
Date-Modified = {2020-07-11 17:50:29 +0200},
Doi = {https://doi.org/10.1006/jfan.1995.1027},
Issn = {0022-1236},
Journal = {J. Funct. Anal.},
Number = {1},
Pages = {163 - 185},
Title = {Endpoint Estimates for Commutators of Singular Integral Operators},
Url = {http://www.sciencedirect.com/science/article/pii/S0022123685710270},
Volume = {128},
Year = {1995},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0022123685710270},
Bdsk-Url-2 = {https://doi.org/10.1006/jfan.1995.1027}}
@article{Guo2019,
Author = {Guo, Weichao and Lian, Jiali and Wu, Huoxiong},
Date-Added = {2020-04-15 13:15:38 +0200},
Date-Modified = {2020-07-11 17:20:35 +0200},
Doi = {10.1007/s12220-019-00226-y},
Journal = {J. Geom. Anal.},
Month = {09},
Title = {The Unified Theory for the Necessity of Bounded Commutators and Applications},
Year = {2017},
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Bdsk-Url-1 = {https://doi.org/10.1007/s12220-019-00226-y}}
@article{Accomazzo2018,
Author = {Accomazzo, Natalia},
Date-Added = {2020-04-15 12:43:11 +0200},
Date-Modified = {2020-07-11 16:07:29 +0200},
Doi = {10.1007/s11856-018-1778-x},
Journal = {Isr. J. Math.},
Month = {02},
Pages = {787--800},
Title = {A characterization of $\mathrm{BMO}$ in terms of endpoint bounds for commutators of singular integrals},
Volume = {228},
Year = {2018},
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Bdsk-Url-1 = {https://doi.org/10.1007/s11856-018-1778-x}}
@article{Riesz1949,
Author = {Riesz, Marcel},
Date-Added = {2020-04-14 18:07:42 +0200},
Date-Modified = {2020-07-11 17:52:49 +0200},
Journal = {Acta Math.},
Pages = {1--223},
Title = {L'int\'egrale de Riemann-Liouville et le probl\`eme de Cauchy},
Volume = {81},
Year = {1949}}
@article{Riesz1938,
Author = {Riesz, Marcel},
Date-Added = {2020-04-14 18:07:16 +0200},
Date-Modified = {2020-07-10 12:34:22 +0200},
Journal = {Acta Sci. Math. Szeged},
Number = {1},
Pages = {1--42},
Title = {Int{\'e}grales de Riemann-Liouville et potentiels},
Volume = {9},
Year = {1938}}
@article{Liouville1832-2,
Author = {Liouville, Joseph},
Date-Added = {2020-04-14 18:02:47 +0200},
Date-Modified = {2020-07-11 17:43:19 +0200},
Journal = {J. {\'E}c. polytech. Math.},
Pages = {71--62},
Title = {M\'emoire sur le calcul des diff\'erentielles indices quelconques.},
Year = {1832}}
@article{Liouville1832,
Author = {Liouville, Joseph},
Date-Added = {2020-04-14 17:59:56 +0200},
Date-Modified = {2020-07-11 17:42:44 +0200},
Journal = {J. {\'E}c. polytech. Math.},
Number = {XXI},
Pages = {1--69},
Title = {M\'moire sur quelques Qu\'estions de G\'eometrie et de M\'ecanique, et sur un nouveau genre de Calcul pour r\'esoudre ces Qu\'estions},
Volume = {XIII}}
@incollection{Riemann1847,
Author = {Riemann, Bernhard},
Booktitle = {Gesammelte mathematische Werke},
Date-Added = {2020-04-14 17:42:13 +0200},
Date-Modified = {2020-07-11 17:52:26 +0200},
Editor = {Dedekind, Richard and Weber, Heinrich Martin},
Title = {Versuch einer allgemeinen Auffassung der Integration und Differentiation (1847)},
Year = {1876},
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@article{Dugowson1997,
Author = {Dugowson, St\'ephane},
Date-Added = {2020-04-14 17:30:59 +0200},
Date-Modified = {2020-07-11 17:10:22 +0200},
Journal = {Rev. Hist. Math.},
Language = {fr},
Number = {1},
Pages = {49-97},
Publisher = {Soci\'et\'e math\'ematique de France},
Title = {L'\'elaboration par Riemann d'une d\'efinition de la d\'erivation d'ordre non entier},
Url = {http://www.numdam.org/item/RHM_1997__3_1_49_0},
Volume = {3},
Year = {1997},
Zbl = {0881.01007},
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Bdsk-Url-1 = {http://www.numdam.org/item/RHM_1997__3_1_49_0}}
@article{Lutzen1982,
Abstract = {It is well known that Liouville did pioneering work on the application of specific integral equations in different parts of mathematics and mathematical physics. However, his short paper on spectral theory of Hilbert-Schmidt like operators has been neglected. With that paper Liouville initiated the general theory of integral equations.
R{\'e}sum{\'e}
Il est bien connu que Joseph Liouville {\'e}tait parmi les premiers {\`a} appliquer des {\'e}quations int{\'e}grales {\`a} la solution de plusieurs probl{\`e}ms de math{\'e}matique et de m{\'e}chanique. D'autre part, sa note sur la th{\'e}orie spectrale des op{\'e}rateurs du type Hilbert-Schmidt est rest{\'e}e inconnue. Dans cette note, Liouville {\`a} entam{\'e} la th{\'e}orie g{\'e}n{\'e}rale des {\'e}quations int{\'e}grales.},
Author = {Jesper L\"utzen},
Date-Added = {2020-04-14 13:30:30 +0200},
Date-Modified = {2020-07-11 17:44:53 +0200},
Doi = {https://doi.org/10.1016/0315-0860(82)90104-5},
Issn = {0315-0860},
Journal = {Historia Math.},
Number = {4},
Pages = {373 - 391},
Title = {Joseph Liouville's contribution to the theory of integral equations},
Url = {http://www.sciencedirect.com/science/article/pii/0315086082901045},
Volume = {9},
Year = {1982},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0315086082901045},
Bdsk-Url-2 = {https://doi.org/10.1016/0315-0860(82)90104-5}}
@article{Luque2015,
Author = {Luque, Teresa and P\'erez, Carlos and Rela, Ezequiel},
Date-Added = {2020-04-13 16:08:12 +0200},
Date-Modified = {2020-04-13 16:08:23 +0200},
Fjournal = {Mathematical Research Letters},
Issn = {1073-2780},
Journal = {Math. Res. Lett.},
Mrclass = {42B25 (42B35)},
Mrnumber = {3342184},
Mrreviewer = {Huoxiong Wu},
Number = {1},
Pages = {183--201},
Title = {Optimal exponents in weighted estimates without examples},
Url = {https://doi.org/10.4310/MRL.2015.v22.n1.a10},
Volume = {22},
Year = {2015},
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Bdsk-Url-1 = {https://doi.org/10.4310/MRL.2015.v22.n1.a10}}
@article{CruzUribe2013,
Author = {Cruz-Uribe, David and Moen, Kabe},
Date-Added = {2020-04-13 16:07:48 +0200},
Date-Modified = {2020-04-13 16:07:48 +0200},
Fjournal = {Illinois Journal of Mathematics},
Issn = {0019-2082},
Journal = {Illinois J. Math.},
Mrclass = {42B25 (42B30 42B35)},
Mrnumber = {3224572},
Mrreviewer = {Yasuo Komori-Furuya},
Number = {1},
Pages = {295--323},
Title = {One and two weight norm inequalities for {R}iesz potentials},
Url = {http://projecteuclid.org/euclid.ijm/1403534497},
Volume = {57},
Year = {2013},
Bdsk-Url-1 = {http://projecteuclid.org/euclid.ijm/1403534497}}
@article{Coifman1976,
Author = {Coifman, Ronald R. and Rochberg, Richard and Weiss, Guido},
Date-Added = {2020-04-13 16:07:37 +0200},
Date-Modified = {2020-07-11 17:05:57 +0200},
Doi = {10.2307/1970954},
Journal = {Ann. Math.},
Month = {5},
Number = {3},
Pages = {611--635},
Publisher = {{JSTOR}},
Title = {Factorization Theorems for Hardy Spaces in Several Variables},
Volume = {103},
Year = {1976},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {https://doi.org/10.2307/1970954}}
@article{Holmes2015,
Author = {Holmes, Irina and Wick, Brett D.},
Date-Added = {2020-04-13 16:02:10 +0200},
Date-Modified = {2020-07-11 17:28:10 +0200},
Journal = {J. Operator Theory},
Title = {Two Weight Inequalities for Iterated Commutators with Calder\'on--Zygmund Operators},
Volume = {79},
Year = {2015}}
@article{CruzUribe2012,
Author = {Cruz-Uribe, David and Moen, Kabe},
Date-Added = {2020-04-13 16:00:01 +0200},
Date-Modified = {2020-07-11 17:08:47 +0200},
Doi = {10.5565/publmat_56112_06},
Journal = {Publicacions Mat.},
Month = {1},
Pages = {147--190},
Publisher = {Universitat Autonoma de Barcelona},
Title = {Sharp norm inequalities for commutators of classical operators},
Volume = {56},
Year = {2012},
Bdsk-Url-1 = {https://doi.org/10.5565/publmat_56112_06}}
@article{Benyi2020,
Abstract = {We present a unified method to obtain unweighted and weighted estimates of linear and multilinear commutators with BMO functions, that is amenable to a plethora of operators and functional settings. Our approach elaborates on a commonly used Cauchy integral trick, recovering many known results but yielding also numerous new ones. In particular, we solve a problem about the boundedness of the commutators of the bilinear Hilbert transform with functions in BMO.},
Author = {B\'enyi, \'Arp\'ad and Martell, Jos{\'{e}} Mar{\'{\i}}a and Moen, Kabe and Stachura, Eric and Torres, Rodolfo H.},
Da = {2020/02/01},
Date-Added = {2020-04-13 15:59:50 +0200},
Date-Modified = {2020-07-11 16:46:19 +0200},
Doi = {10.1007/s00208-019-01870-z},
Id = {B{\'e}nyi2020},
Isbn = {1432-1807},
Journal = {Math. Ann.},
Number = {1},
Pages = {61--102},
Title = {Boundedness results for commutators with BMO functions via weighted estimates: a comprehensive approach},
Ty = {JOUR},
Url = {https://doi.org/10.1007/s00208-019-01870-z},
Volume = {376},
Year = {2020},
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Bdsk-Url-1 = {https://doi.org/10.1007/s00208-019-01870-z}}
@article{CruzUribe2002,
Author = {Cruz-Uribe, David and P{\'{e}}rez, Carlos},
Date-Added = {2020-04-10 18:09:01 +0200},
Date-Modified = {2020-04-10 18:09:01 +0200},
File = {:Users/jmartinez/Desktop/Art{\'{i}}culos y Libros/Cruz-uribe, P{\'{e}}rez/2002/Annali Scuola Normale Superiore di Pisa/Cruz-uribe, P{\'{e}}rez - 2002 - On the Two-weight Problem for Singular Integral Operators.pdf:pdf},
Journal = {Ann. Scuola. Norm.-Sci.},
Number = {5},
Pages = {821--849},
Title = {{On the Two-weight Problem for Singular Integral Operators}},
Volume = {I},
Year = {2002},
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@article{CruzUribe2000,
Author = {Cruz-Uribe, David and P{\'{e}}rez, Carlos},
Date-Added = {2020-04-10 18:08:47 +0200},
Date-Modified = {2020-04-10 18:08:47 +0200},
Journal = {Indiana U. Math. J.},
Number = {2},
Pages = {697--721},
Title = {{Two-weight, Weak-type Norm Inequalities for Fractional Integrals, Calder\'on-Zygmund Operators and Commutators}},
Volume = {49},
Year = {2000}}
@article{Dyda2006,
Author = {Dyda, Bart\l{}omiej},
Date-Added = {2020-04-10 18:05:55 +0200},
Date-Modified = {2020-07-11 17:11:19 +0200},
Journal = {J. Math. Anal. Appl.},
Pages = {564-577},
Title = {On comparability of integral forms},
Volume = {318},
Year = {2006}}
@article{Campanato1963,
Author = {Campanato, Sergio},
Date-Added = {2020-04-10 18:03:47 +0200},
Date-Modified = {2020-04-10 18:03:47 +0200},
Journal = {Ann. Scuola. Norm.-Sci.},
Mrnumber = {156188},
Number = {1-2},
Pages = {175-188},
Publisher = {Scuola normale superiore},
Title = {Propriet\`a di h\"olderianit\`a di alcune classi di funzioni},
Url = {http://www.numdam.org/item/ASNSP_1963_3_17_1-2_175_0},
Volume = {Ser. 3, 17},
Year = {1963},
Zbl = {0121.29201},
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Bdsk-Url-1 = {http://www.numdam.org/item/ASNSP_1963_3_17_1-2_175_0}}
@article{Zhou2014,
Author = {Zhou, Yuan},
Booktitle = {Transactions of the American Mathematical Society},
Date-Added = {2020-04-10 17:25:56 +0200},
Date-Modified = {2020-07-11 17:58:53 +0200},
Journal = {Trans. Amer. Math. Soc.},
Month = {02},
Pages = {959-979},
Title = {Fractional Sobolev extension and imbedding},
Volume = {367},
Year = {2015}}