Frontiers of Mathematics in China >

2013 , Vol. 8 >Issue 4: 961 - 971

DOI: https://doi.org/10.1007/s11464-013-0210-4

RESEARCH ARTICLE

Boundedness of Calderón-Zygmund operators with finite non-doubling measures

  • Dachun YANG 1 ,
  • Dongyong YANG , 2
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  • 1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex systems, Ministry of Education, Beijing 100875, China
  • 2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received date: 15 Jan 2012

Accepted date: 06 Apr 2012

Published date: 01 Aug 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

Let μ be a nonnegative Radon measure on ℝd which satisfies the polynomial growth condition that there exist positive constants C0 and n ∈ (0, d] such that, for all x ∈ ℝd and r>0, μ(B(x, r))≤C0rn, where B(x, r) denotes the open ball centered at x and having radius r. In this paper, we show that, if μ(ℝd)<∞, then the boundedness of a Calderón-Zygmund operator T on L2(μ) is equivalent to that of T from the localized atomic Hardy space h1(μ) to L1,∞(μ) or from h1(μ) to L1(μ).

Key words： Calderón-Zygmund operator; localized atomic Hardy space; nondoubling measure

Cite this article

Dachun YANG , Dongyong YANG . Boundedness of Calderón-Zygmund operators with finite non-doubling measures[J]. Frontiers of Mathematics in China, 2013 , 8(4) : 961 -971 . DOI: 10.1007/s11464-013-0210-4

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