A generalization of Hardy spaces Hp by using atoms

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 Macías and Segovia. We also study the relations of our function spaces for (X, d, μ) and (X, δ, μ). This research is partially supported by Grant-in-Aid for Exploratory Research, No. 17654033, the Ministry of Education, Culture, Sports, Science and Technology, Japan, and, Grant-in-Aid for Scientific Research (C), No. 20540167, Japan Society for the Promotion of Science