On integral operators in weighted grand Lebesgue spaces of Banach‐valued functions

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.

Rubio de Francia Extrapolation Theorems for Quasi-Monotone Functions

“…We refer to [15] and the references therein. For some very recent updates on grand Lebesgue spaces, we mention [8], [11], [14], [17], [18], [19], [23].…”