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Hardy spaces of spaces of homogeneous type

Author(s): Xuan Thinh Duong; Lixin Yan
Journal: Proc. Amer. Math. Soc. 131 (2003), 3181-3189.
MSC (2000): Primary 42B20, 42B30, 47G10
Posted: February 14, 2003
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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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Additional Information:

Xuan Thinh Duong
Affiliation: Department of Mathematics, Macquarie University, New South Wales 2109, Australia
Email: duong@ics.mq.edu.au

Lixin Yan
Affiliation: Department of Mathematics, Macquarie University, New South Wales 2109, Australia -- and -- Department of Mathematics, Zhongshan University, Guangzhou, 10275, People's Republic of China
Email: lixin@ics.mq.edu.au

DOI: 10.1090/S0002-9939-03-06868-0
PII: S 0002-9939(03)06868-0
Keywords: Spaces of homogeneous type, Hardy spaces, semigroup, Calder\'on-type reproducing formula, atomic decomposition
Received by editor(s): January 24, 2002
Received by editor(s) in revised form: May 16, 2002
Posted: February 14, 2003
Additional Notes: Both authors were partially supported by a grant from Australia Research Council, and the second author was also partially supported by the NSF of China
Communicated by: Andreas Seeger
Copyright of article: Copyright 2003, American Mathematical Society

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