Boundedness of the Hardy-Littlewood maximal operator on generalized fofana spaces

TL;DR

This paper introduces generalized Fofana spaces, extending Morrey spaces, and proves the Hardy-Littlewood maximal operator is bounded on these new spaces.

Contribution

The paper defines generalized Fofana spaces and demonstrates the boundedness of the Hardy-Littlewood maximal operator on them.

Findings

Generalized Fofana spaces are a new class extending Morrey spaces.

Boundedness of the Hardy-Littlewood maximal operator is established on these spaces.

Basic properties of the generalized Fofana spaces are analyzed.

Abstract

We introduce generalized Fofana spaces and we give some of their basic properties. These spaces are a kind of generalization of generalized Morrey spaces. As application, we establish the boundedness of the Hardy-Littlewood maximal operator on these new spaces.