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On integral operators in weighted grand Lebesgue spaces of Banach‐valued functions
Author(s) -
Kokilashvili Vakhtang,
Meskhi Alexander
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6779
Subject(s) - mathematics , singular integral operators of convolution type , lp space , multiplier (economics) , diagonal , lebesgue integration , riemann integral , lebesgue's number lemma , pure mathematics , daniell integral , maximal function , absolute continuity , norm (philosophy) , lebesgue measure , banach space , mathematical analysis , operator theory , fourier integral operator , microlocal analysis , geometry , law , political science , economics , macroeconomics
The paper deals with boundedness problems of integral operators in weighted grand Bochner‐Lebesgue spaces. We will treat both cases: when a weight function appears as a multiplier in the definition of the norm, or when it defines the absolute continuous measure of integration. Along with the diagonal case, we deal with the off‐diagonal case. To get the appropriate result for the Hardy‐Littlewood maximal operator, we rely on the reasonable bound of the sharp constant in the Buckley‐type theorem, which is also derived in the paper.