Comparison of Hardy-Littlewood and Dyadic Maximal Functions on Spaces of Homogeneous Type

Hugo A. Aimar, Ana L. Bernardis, Bibiana Iaffei


We obtain a comparison of the level sets for two maximal functions on a space of homogeneous type: the Hardy-Littlewood maximal function of mean values over balls and the dyadic maximal function of mean values over the
dyadic sets introduced by M. Christ in [4]. As applications to the theory of Ap weights on this setting, we compare the standard and the dyadic Muckenhoupt
classes and we give an alternative proof of reverse Hölder type inequalities.

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