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The Hardy space H1 on non-homogeneous metric spaces

Published online by Cambridge University Press:  08 December 2011

TUOMAS HYTÖNEN ,
DACHUN YANG  and
DONGYONG YANG
TUOMAS HYTÖNEN
Affiliation:
Department of Mathematics and Statistics, P.O.B. 68, (Gustaf Hällströmin katu 2b), FI-00014 University of Helsinki, Finland. e-mail: tuomas.hytonen@helsinki.fi
DACHUN YANG*
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex systems, Ministry of Education, Beijing 100875, People's Republic of China. e-mail: dcyang@bnu.edu.cn
DONGYONG YANG
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, People's Republic of China. e-mail: dyyang@xmu.edu.cn
*
Corresponding author
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Abstract

Let (, d, μ) be a metric measure space and satisfy the so-called upper doubling condition and the geometrical doubling condition. We introduce the atomic Hardy space H1(μ) and prove that its dual space is the known space RBMO(μ) in this context. Using this duality, we establish a criterion for the boundedness of linear operators from H1(μ) to any Banach space. As an application of this criterion, we obtain the boundedness of Calderón–Zygmund operators from H1(μ) to L1(μ).

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 153 , Issue 1 , July 2012 , pp. 9 - 31
Copyright
Copyright © Cambridge Philosophical Society 2011

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