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