Hardy spaces of spaces of homogeneous type

Duong, Xuan; Yan, Lixin

doi:10.1090/S0002-9939-03-06868-0

Hardy spaces of spaces of homogeneous type
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by Xuan Thinh Duong and Lixin Yan PDF

Proc. Amer. Math. Soc. 131 (2003), 3181-3189 Request permission

Abstract:

Let $X$ be a space of homogeneous type, and $L$ be the generator of a semigroup with Gaussian kernel bounds on $L^2(X)$. We define the Hardy spaces $H^p_s(X)$ of $X$ for a range of $p$, by means of area integral function associated with the Poisson semigroup of $L$, which is proved to coincide with the usual atomic Hardy spaces $H^p_{at}(X)$ on spaces of homogeneous type.

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