Hardy spaces of spaces of homogeneous type

Authors:
Xuan Thinh Duong and Lixin Yan

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3181-3189

MSC (2000):
Primary 42B20, 42B30, 47G10

DOI:
https://doi.org/10.1090/S0002-9939-03-06868-0

Published electronically:
February 14, 2003

MathSciNet review:
1992859

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a space of homogeneous type, and be the generator of a semigroup with Gaussian kernel bounds on . We define the Hardy spaces of for a range of , by means of area integral function associated with the Poisson semigroup of , which is proved to coincide with the usual atomic Hardy spaces 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:
https://doi.org/10.1090/S0002-9939-03-06868-0

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

Published electronically:
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

Article copyright:
© Copyright 2003
American Mathematical Society