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

Abstract

In this article we characterize all possible cases that may occur in the rela- tions 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.