Radial maximal function characterizations for Hardy spaces on RD-spaces
An RD-space is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds. The authors prove that for a space of homogeneous type having “dimension” , there exists a such that for certain classes of distributions, the quasi-norms of their radial maximal functions and grand maximal functions are equivalent when . This result yields a radial maximal function characterization for Hardy spaces on .