A note on boundedness of the Hardy-Littlewood maximal operator on Morrey spaces

TL;DR

This paper proves that the Hardy-Littlewood maximal operator is bounded on Morrey spaces for radial, decreasing functions, extending understanding of maximal operator behavior in these function spaces.

Contribution

It establishes boundedness of the Hardy-Littlewood maximal operator on Morrey spaces specifically for radial, decreasing functions, a case not previously fully addressed.

Findings

Maximal operator is bounded on Morrey spaces for radial, decreasing functions

Extends known boundedness results to a specific class of functions in Morrey spaces

Provides theoretical foundation for further analysis of maximal operators in Morrey spaces

Abstract

In this paper we prove that the Hardy-Littlewood maximal operator is bounded on Morrey spaces $\mathcal{M}_{1,\lambda}(\rn)$, $0 \le \la < n$ for radial, decreasing functions on $\rn$