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• W1977652103 abstract "Let $${{mathcal X}}$$ be an RD-space with $${mu({mathcal X})=infty}$$ , which means that $${{mathcal X}}$$ is a space of homogeneous type in the sense of Coifman and Weiss and its measure has the reverse doubling property. In this paper, we characterize the atomic Hardy spaces $${H^p_{rm at}({mathcal X})}$$ of Coifman and Weiss for $${pin(n/(n+1),1]}$$ via the radial maximal function, where n is the “dimension” of $${{mathcal X}}$$ , and the range of index p is the best possible. This completely answers the question proposed by Ronald R. Coifman and Guido Weiss in 1977 in this setting, and improves on a deep result of Uchiyama in 1980 on an Ahlfors 1-regular space and a recent result of Loukas Grafakos et al in this setting. Moreover, we obtain a maximal function theory of localized Hardy spaces in the sense of Goldberg on RD-spaces by generalizing the above result to localized Hardy spaces and establishing the links between Hardy spaces and localized Hardy spaces. These results have a wide range of applications. In particular, we characterize the Hardy spaces $${H^p_{rm at}(M)}$$ via the radial maximal function generated by the heat kernel of the Laplace-Beltrami operator Δ on complete noncompact connected manifolds M having a doubling property and supporting a scaled Poincaré inequality for all $${pin(n/(n+alpha),1]}$$ , where α represents the regularity of the heat kernel. This extends some recent results of Russ and Auscher-McIntosh-Russ." @default.
• W1977652103 created "2016-06-24" @default.
• W1977652103 creator A5045927034 @default.
• W1977652103 creator A5068607724 @default.
• W1977652103 date "2009-08-06" @default.
• W1977652103 modified "2023-10-15" @default.
• W1977652103 title "Radial maximal function characterizations of Hardy spaces on RD-spaces and their applications" @default.
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• W1977652103 doi "https://doi.org/10.1007/s00208-009-0400-2" @default.
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