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

TL;DR

This paper characterizes the possible relationships between weak and strong type inequalities for Hardy--Littlewood maximal operators in general metric measure spaces, extending understanding beyond classical doubling measure contexts.

Contribution

It provides a comprehensive classification of all potential cases relating weak and strong type inequalities for maximal operators in non-doubling metric measure spaces.

Findings

Identifies all possible relations between weak and strong type inequalities.

Extends classical results to non-doubling metric measure spaces.

Provides a complete characterization of these relations.

Abstract

In this article we characterize all possible cases that may occur in the relations between the sets of $p$ for which weak type $(p,p)$ and strong type $(p,p)$ inequalities for the Hardy--Littlewood maximal operators, both centered and non-centered, hold in the context of general metric measure spaces.