1. On integral operators in weighted grand Lebesgue spaces of Banach-valued functions
- Author
-
Alexander Meskhi and Vakhtang Kokilashvili
- Subjects
Mathematics::Functional Analysis ,Pure mathematics ,Weight function ,General Mathematics ,010102 general mathematics ,Diagonal ,Mathematics::Classical Analysis and ODEs ,General Engineering ,Singular integral ,01 natural sciences ,Measure (mathematics) ,010101 applied mathematics ,Multiplier (Fourier analysis) ,Maximal function ,0101 mathematics ,Lp space ,Constant (mathematics) ,Mathematics - Abstract
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.
- Published
- 2020