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A generalization of Hardy spaces H p by using atoms

  • Eiichi Nakai
Article

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 Macías and Segovia. We also study the relations of our function spaces for (X, d, µ) and (X, δ, µ).

Keywords

Hardy space Hardy-Orlicz space variable exponent Campanato space space of homogeneous type 

MR(2000) Subject Classification

42B30 46E30 42B35 46E15 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Department of MathematicsOsaka Kyoiku UniversityKashiwara, OsakaJapan

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