Access the full text.
Sign up today, get DeepDyve free for 14 days.
L. Grafakos (2010)
Classical Fourier Analysis
D. Cruz-Uribe, Jeremy Cummings (2020)
Weighted norm inequalities for the maximal operator on L^p(·) over spaces of homogeneous typeAnnales Fennici Mathematici
O. Toivanen (2014)
Lebesgue and Sobolev spaces with variable exponents
L Diening, P Harjulehto, P Hästö, M Ružička (2011)
10.1007/978-3-642-18363-8Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Math
V. Kokilashvili, A. Meskhi, H. Rafeiro, S. Samko (2016)
Integral Operators in Non-Standard Function Spaces
L. Diening, P. Hästö (2011)
MUCKENHOUPT WEIGHTS IN VARIABLE EXPONENT SPACES
P. Hajłasz, P. Koskela (2000)
Sobolev met Poincaré
D. Cruz-Uribe, A. Fiorenza (2013)
Variable Lebesgue Spaces
A. Fiorenza, V. Kokilashvili, A. Meskhi (2017)
Hardy–Littlewood Maximal Operator in Weighted Grand Variable Exponent Lebesgue SpaceMediterranean Journal of Mathematics, 14
Sfo Cruz-Uribe, A. Fiorenza, C. Neugebauer (2012)
Weighted norm inequalities for the maximal operator on variable Lebesgue spacesJournal of Mathematical Analysis and Applications, 394
(1979)
The topology of the space Lp(t) ([0,1]) (in Russian)
G. Pradolini, O. Salinas (2007)
Commutators of singular integrals on spaces of homogeneous typeCzechoslovak Mathematical Journal, 57
D. Cruz-Uribe, A. Fiorenza (2013)
Variable Lebesgue Spaces: Foundations and Harmonic Analysis
V. Kokilashvili, V. Paatashvili (2012)
Boundary value problems for analytic and harmonic functions in nonstandard Banach function spaces
D. Edmunds, V. Kokilashvili, A. Meskhi (2019)
Sobolev‐type inequalities for potentials in grand variable exponent Lebesgue spacesMathematische Nachrichten, 292
V. Kokilashvili, A. Meskhi (2016)
Weighted extrapolation in Iwaniec—Sbordone spaces. Applications to integral operators and approximation theoryProceedings of the Steklov Institute of Mathematics, 293
T. Hytonen, C. P'erez, E. Rela (2012)
Sharp Reverse H\"older property for A_\infty weights on spaces of homogeneous typearXiv: Classical Analysis and ODEs
T. Iwaniec, C. Sbordone (1992)
On the integrability of the Jacobian under minimal hypothesesArchive for Rational Mechanics and Analysis, 119
V. Kokilashvili, A. Meskhi, H. Rafeiro, S. Samko (2016)
Variable exponent hölder, morrey : campanato and grand spaces
J. Strömberg, A. Torchinsky (1989)
Weighted Hardy Spaces
K. Brown, Hsiao-Lan Liu (1982)
Graduate Texts in Mathematics
(1951)
Topology of Linear Topological Spaces
D. Cruz-Uribe, O. Guzmán (2018)
Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spacesPublicacions Matemàtiques
S. Samko (1998)
Convolution type operators in lp (x)Integral Transforms and Special Functions, 7
G. David (1984)
Opérateurs intégraux singuliers sur certaines courbes du plan complexeAnnales Scientifiques De L Ecole Normale Superieure, 17
D. Cruz-Uribe, Parantap Shukla (2015)
The Boundedness of fractional maximal operators on variable Lebesgue spaces over spaces of homogeneous typearXiv: Classical Analysis and ODEs
V. Kokilashvili, S. Samko (2003)
Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent, 10
R. Coifman, Guido Weiss (1971)
Analyse harmonique non-commutative sur certains espaces homogènes : étude de certaines intégrales singulières
D. Cruz-Uribe, L. Wang (2014)
Extrapolation and weighted norm inequalities in the variable Lebesgue spacesTransactions of the American Mathematical Society, 369
L. Diening (2004)
Maximal function on generalized Lebesgue spaces $L^{p(\cdot)}$Mathematical Inequalities & Applications, 7
A. Fiorenza (2000)
Duality and reflexivity in grand Lebesgue spacesCollectanea Mathematica, 51
V. Kokilashvili, S. Samko (2004)
Maximal and Fractional Operators in Weighted $L^{p(x)}$ SpacesRevista Matematica Iberoamericana, 20
D. Cruz-Uribe, A. Fiorenza, J. Martell, C. Pérez (2006)
THE BOUNDEDNESS OF CLASSICAL OPERATORS ON VARIABLE L p SPACESAnnales Academiae Scientiarum Fennicae. Mathematica, 31
O. Kováčik, J. Rákosnik (1991)
On spaces $L^{p(x)}$ and $W^{k, p(x)}$Czechoslovak Mathematical Journal, 41
V. Kokilashvili, A. Meskhi (2009)
A Note on the Boundedness of the Hilbert Transform in Weighted Grand Lebesgue Spaces, 16
D. Deng, Yongsheng Han, Y. Meyer (2008)
Harmonic Analysis on Spaces of Homogeneous Type
L. Greco, T. Iwaniec, C. Sbordone (1997)
Inverting thep-harmonic operatormanuscripta mathematica, 92
M. Bramanti, M. Cerutti (1996)
Commutators of singular integrals on homogeneous spaces, 10
V. Kokilashvili, A. Meskhi (2014)
Maximal and Calderón–Zygmund operators in grand variable exponent Lebesgue spacesGeorgian Mathematical Journal, 21
R. Coifman, Guido Weiss (1971)
Analyse Hamonique Non-Commutative sur Certains Espaces Homogenes
J. Duoandikoetxea (2011)
Extrapolation of weights revisited: New proofs and sharp boundsJournal of Functional Analysis, 260
V. Kokilashvili, A. Meskhi, H. Rafeiro, S. Samko (2016)
Hardy-type Operators in Variable Exponent Lebesgue Spaces
A. Fiorenza, Babita Gupta, P. Jain (2008)
The maximal theorem for weighted grand Lebesgue spacesStudia Mathematica, 188
Petteri Harjulehto, P. Hästö, M. Pere (2005)
Variable Exponent Lebesgue Spaces on Metric Spaces: The Hardy-Littlewood Maximal OperatorReal analysis exchange, 30
R. Macías, C. Segovia (1979)
Lipschitz functions on spaces of homogeneous typeAdvances in Mathematics, 33
V. Kokilashvili, S. Samko (2008)
The Maximal Operator in Weighted Variable Exponent Spaces on Metric Spaces, 15
Weighted inequalities with power-type weights for operators of harmonic analysis, such as maximal and singular integral operators, and commutators of singular integrals in grand variable exponent Lebesgue spaces are derived. The spaces and operators are defined on quasi-metric measure spaces with doubling condition (spaces of homogeneous type). The proof of the result regarding the Hardy–Littlewood maximal operator is based on the appropriate sharp weighted norm estimates with power-type weights. To obtain the results for singular integrals and commutators we prove appropriate weighted extrapolation statement in grand variable exponent Lebesgue spaces. The extrapolation theorem deals with a family of pairs of functions (f, g). One of the consequences of the latter result is the weighted extrapolation for sublinear operators S acting in these spaces. As one of the applications of the main results we present weighted norm estimates for the Hardy–Littlewood maximal function, Cauchy singular integral operator, and its commutators in grand variable exponent Lebesgue spaces defined on rectifiable regular curves.
Annals of Functional Analysis – Springer Journals
Published: Jun 14, 2021
Keywords: Weighted grand variable exponent Lebesgue spaces; Weighted extrapolation; Maximal operator; Singular integrals; Commutators; 42B20; 42B25; 47B38
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.