Grand variable Herz-Morrey-Hardy Spaces and applications to the boundedness of integral operators

TL;DR

This paper introduces grand variable Herz-Morrey-Hardy spaces, provides their atomic characterization, and studies the boundedness of singular integral operators and commutators within these spaces.

Contribution

It presents a novel class of function spaces and establishes their atomic structure, enabling analysis of integral operators and commutators.

Findings

Atomic characterization of grand variable Herz-Morrey-Hardy spaces

Boundedness of singular integral operators on these spaces

Lipschitz estimates for commutators of fractional integrals

Abstract

In this paper, the concept of grand variable Herz-Morrey-Hardy spaces are introduced. We also establish the atomic characterization of these spaces. As an application the authors investigate the continuity of a few singular integral operators. We also obtain the boundedness of commutators of homogeneous fractional integrals and their Lipschitz estimate on these spaces by applying the characterization.