The Hardy-Littlewood Maximal Operator on Discrete Morrey Spaces

TL;DR

This paper investigates the boundedness of the Hardy-Littlewood maximal operator and Riesz potentials on discrete Morrey spaces across various dimensions, utilizing a discrete Fefferman-Stein inequality.

Contribution

It introduces the boundedness of these operators on discrete Morrey spaces, extending classical results to a discrete setting with new inequalities.

Findings

Boundedness of Hardy-Littlewood maximal operator on discrete Morrey spaces

Boundedness of Riesz potentials on discrete Morrey spaces

Application of discrete Fefferman-Stein inequality

Abstract

We discuss the Hardy-Littlewood maximal operator on discrete Morrey spaces of arbitrary dimension. In particular, we obtain its boundedness on the discrete Morrey spaces using a discrete version of the Fefferman-Stein inequality. As a corollary, we also obtain the boundedness of some Riesz potentials on discrete Morrey spaces.