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.2010 Mathematics Subject Classification: Primary 42B25, 46E30.

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].

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