On relations between weak and restricted weak type inequalities for maximal operators on non-doubling metric measure spaces

TL;DR

This paper investigates the differences between weak and restricted weak type inequalities for maximal operators on certain non-doubling metric measure spaces, extending previous results.

Contribution

It identifies a class of non-doubling spaces where weak and restricted weak type inequalities differ significantly, extending earlier findings.

Findings

Significant differences between weak and restricted weak type inequalities in specific non-doubling spaces

Extension of previous results on maximal operators in non-doubling metric measure spaces

Analysis of centered and non-centered Hardy--Littlewood maximal operators

Abstract

In this article we study a special class of non-doubling metric measure spaces for which there is a significant difference between the incidence of weak and restricted weak type $(p,p)$ inequalities for the centered and non-centered Hardy--Littlewood maximal operators, $M^c$ and $M$. As a corollary we extend the result obtained in [2].