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Boundedness of Calderon-Zygmund Operators on Non-homogeneous Metric Measure Spaces

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Boundedness of Calderon-Zygmund Operators on Non-homogeneous Metric Measure Spaces.htm (388bytes)
Date
2012-08
Author
Hytonen, Tuomas
Liu, Suile
Yang, Dachun
Yang, Dongyong
杨东勇
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  • 数学科学-已发表论文 [2679]
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Abstract
Let (X, d, mu) be a separable metric measure space satisfying the known upper doubling condition, the geometrical doubling condition, and the non-atomic condition that mu({x}) = 0 for all x is an element of X. In this paper, we show that the boundedness of a Calderon-Zygmund operator T on L-2(mu) is equivalent to that of T on L-p(mu) for some p is an element of (1, infinity), and that of T from L-1(mu) to L-1,L- infinity (mu). As an application, we prove that if T is a Calderon-Zygmund operator bounded on L-2(mu), then its maximal operator is bounded on L-p(mu) for all p is an element of (1, infinity) and from the space of all complex-valued Borel measures on X to L-1,L- infinity (mu). All these results generalize the corresponding results of Nazarov et al. on metric spaces with measures satisfying the so-called polynomial growth condition.
Citation
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,2012,64(4):892-923
URI
http://dx.doi.org/10.4153/CJM-2011-065-2
WOS:000306716600008
https://dspace.xmu.edu.cn/handle/2288/15038

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