Two-weight norm estimates for sublinear integral operators in variable exponent Lebesgue spaces

Vakhtang Kokilashvili; Alexander Meskhi

doi:10.1556/sscmath.51.2014.3.1290

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 51: Issue 3

Two-weight norm estimates for sublinear integral operators in variable exponent Lebesgue spaces

Authors:

Vakhtang Kokilashvili

Vakhtang Kokilashvili

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Alexander Meskhi

Alexander Meskhi

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Pages:: 384–406

Online Publication Date:: 26 Aug 2014

Publication Date:: 01 Sep 2014

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.51.2014.3.1290

Keywords:: Primary 42B20, 42B25, 26A33, 46E30; Sublinear integral operators; maximal operator; singular integrals; fractional integrals; spaces of homogeneous type; variable exponent Lebesgue spaces; two-weight inequality

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Two-weight norm estimates for sublinear integral operators involving Hardy-Littlewood maximal, Calderón-Zygmund and fractional integral operators in variable exponent Lebesgue spaces are derived. Operators and the space are defined on a quasi-metric measure space with doubling condition. The derived conditions are written in terms of L^p(·) norms and are simultaneously necessary and sufficient for appropriate inequalities for maximal and fractional integral operators mainly in the case when weights are of radial type.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

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Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Gábor SÁGI (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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