Comparison of Hardy-Littlewood and dyadic maximal functions on spaces of homogeneous type

[摘要] 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 [M. Christ, A T(b) theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math. 60/61 (1990) 601-628]. As applications to the theory of A(p) weights on this Setting, we compare the standard and the dyadic Muckenhoupt classes and we give an alternative proof of reverse Holder type inequalities. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2005-12-01

[关键词] maximal functions;spaces of homogeneous type;Calderon-Zygmund