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On integral operators in weighted grand Lebesgue spaces of Banach-valued functions
  • Vakhtang Kokilashvili,
  • Alexander Meskhi
Vakhtang Kokilashvili
Ivane Javakhishvili Tbilisi State University
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Alexander Meskhi
Georgian Technical University
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Peer review status:UNDER REVIEW

07 Apr 2020Submitted to Mathematical Methods in the Applied Sciences
13 Apr 2020Assigned to Editor
13 Apr 2020Submission Checks Completed
15 Apr 2020Reviewer(s) Assigned


The paper deals with boundedness problems to 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. Together 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 determined here.