Hardy spaces of spaces of homogeneous type

Abstract

Let X be a space of homogeneous type, and L be the generator of a semigroup with Gaussian kernel bounds on L2(X). We define the Hardy spaces Hsp(X) of X for a range of p, by means of area integral function associated with the Poisson semigroup of L, which is proved to coincide with the usual atomic Hardy spaces Hatp(X) on spaces of homogeneous type.