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Local hardy and BMO spaces on non-homogeneous spaces

Part of: Harmonic analysis in several variables Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Dachun Yang
Dachun Yang
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People's Republic of China, e-mail: dcyang@bnu.edu.cn
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Abstract

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Let µ be Radon measure on Rd which may be non doubling. The only condition that µ must satisfy is the size condition µ(B(x, r)) ≤ Crn for some fixed n є (0, d). Recently, Tolsa introduced the spaces RBMO(µ) and Hatb1.∞ (µ), which, in some ways, play the role of the classical spaces BMO and H1 in case u is a doubling measure. In this paper, the author considers the local versions of the spaces RBMO(µ) and Hatb1.∞ (µ) in the sense of Goldberg and establishes the connections between the spaces RBMO(µ) and Hatb1.∞ (µ) with their local versions. An interpolation result of linear operators is also given.

Keywords

local Hardy spacelcoal B M O spaceatomic blockblocknon-doubling measureinterpolationduality.

MSC classification

Secondary: 42B35: Function spaces arising in harmonic analysis 42B30: $H^p$-spaces 42B25: Maximal functions, Littlewood-Paley theory 43A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 2 , October 2005 , pp. 149 - 182
Copyright
Copyright © Australian Mathematical Society 2005

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