Hardy spaces of spaces of homogeneous type

Xuan Thinh Duong; Lixin Yan

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

Hardy spaces of spaces of homogeneous type

Xuan Thinh Duong, Lixin Yan

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

Let X be a space of homogeneous type, and L be the generator of a semigroup with Gaussian kernel bounds on L²(X). We define the Hardy spaces H_s ^p(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_at ^p(X) on spaces of homogeneous type.

Original language	English
Pages (from-to)	3181-3189
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9939-03-06868-0
Publication status	Published - Oct 2003

Keywords

Atomic decomposition
Calderón-type reproducing formula
Hardy spaces
Semigroup
Spaces of homogeneous type

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10.1090/S0002-9939-03-06868-0

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AB - Let X be a space of homogeneous type, and L be the generator of a semigroup with Gaussian kernel bounds on L2(X). We define the Hardy spaces Hs p(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 Hat p(X) on spaces of homogeneous type.

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KW - Calderón-type reproducing formula

KW - Hardy spaces

KW - Semigroup

KW - Spaces of homogeneous type

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Hardy spaces of spaces of homogeneous type

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Keywords

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