The Hardy-Littlewood Maximal Operator on Discrete Weighted Morrey Spaces

TL;DR

This paper introduces discrete weighted Morrey spaces, explores their properties, and proves the boundedness of discrete Hardy-Littlewood maximal operators on these spaces, extending classical harmonic analysis results to a discrete setting.

Contribution

It develops a discrete framework for weighted Morrey spaces and establishes the boundedness of maximal operators within this new context, which is a novel extension of existing theory.

Findings

Boundedness of discrete Hardy-Littlewood maximal operators on weighted Lebesgue spaces.

Boundedness of maximal operators on discrete weighted Morrey spaces.

Inclusion relations among discrete weighted Morrey spaces.

Abstract

In this paper, we introduce a discrete version of weighted Morrey spaces, and discuss the inclusion relations of these spaces. In addition, we obtain the boundedness of discrete weighted Hardy-Littlewood maximal operators on discrete weighted Lebesgue spaces by establishing a discrete Calder\'on-Zygmund decomposition for weighted $l^1$-sequences. Furthermore, the boundedness of discrete Hardy-Littlewood maximal operators on discrete weighted Morrey spaces is established.