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Littlewood–Paley characterizations for Hardy spaces on spaces of homogeneous type

✍ Scribed by Yongsheng Han; Detlef Müller; Dachun Yang

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
384 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let (𝒳, d,μ) be a space of homogeneous type in the sense of Coifman and Weiss. Assuming that μ satisfies certain estimates from below and there exists a suitable Calderón reproducing formula in L ^2^(𝒳), the authors establish a Lusin‐area characterization for the atomic Hardy spaces H ^p^ ~at~(𝒳) of Coifman and Weiss for p ∈ (p ~0~, 1], where p ~0~ = n /(n + ε ~1~) depends on the “dimension” n of 𝒳 and the “regularity” ε ~1~ of the Calderón reproducing formula. Using this characterization, the authors further obtain a Littlewood–Paley g ^*^~λ~ ‐function characterization for H^p^ (𝒳) when λ > n + 2__n__ /p and the boundedness of Calderón–Zygmund operators on H^p^ (𝒳). The results apply, for instance, to Ahlfors n ‐regular metric measure spaces, Lie groups of polynomial volume growth and boundaries of some unbounded model domains of polynomial type in ℂ^N^ . (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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