Integral Operators in Grand Morrey Spaces

TL;DR

This paper introduces grand Morrey spaces on quasi-metric measure spaces with doubling measures and proves the boundedness of key operators like Hardy--Littlewood maximal, Calderón--Zygmund, and potential operators, extending known results to new settings.

Contribution

It establishes the boundedness of classical operators in grand Morrey spaces on quasi-metric measure spaces, a novel extension even for Euclidean spaces.

Findings

Boundedness of Hardy--Littlewood maximal operator

Boundedness of Calderón--Zygmund operators

Boundedness of potential operators

Abstract

We introduce grand Morrey spaces and establish the boundedness of Hardy--Littlewood maximal, Calder\'on--Zygmund and potential operators in these spaces. In our case the operators and grand Morrey spaces are defined on quasi-metric measure spaces with doubling measure. The results are new even for Euclidean spaces.