A generalization of Hardy spaces H p by using atoms

Abstract

Let X =( X, d, μ) be a space of homogeneous type in the sense of Coifman and Weiss. The purpose of this paper is to generalize the definition of Hardy space H p (X) and prove that the generalized Hardy spaces have the same property as H p (X). Our definition includes a kind of Hardy- Orlicz spaces and a kind of Hardy spaces with variable exponent. The results are new even for the R n case. Let (X, δ, μ) be the normalized space of (X, d, μ) in the sense of Mac´ias and Segovia. We also study the relations of our function spaces for (X, d, μ )a nd (X, δ, μ).