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A NEW CHARACTERIZATION FOR REGULAR BMO WITH NON-DOUBLING MEASURES

Published online by Cambridge University Press:  04 February 2008

Guoen Hu ,
Xin Wang  and
Dachun Yang
Guoen Hu
Affiliation:
Department of Applied Mathematics, University of Information Engineering, PO Box 1001-747, Zhengzhou 450002, China (huguoen@eyou.com)
Xin Wang
Affiliation:
Department of Applied Mathematics, University of Information Engineering, PO Box 1001-747, Zhengzhou 450002, China (huguoen@eyou.com)
Dachun Yang*
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China (dcyang@bnu.edu.cn)
*
Author for correspondence.
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Abstract

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Let $\mu$ be a positive Radon measure on $\mathbb{R}^d$ which satisfies $\mu(B(x,r))\le Cr^{n}$ for any $x\in\mathbb{R}^d$ and $r>0$ and some fixed constants $C>0$ and $n\in(0,d]$. In this paper, a new characterization of the space $\rbmo(\mu)$, which was introduced by Tolsa, is given. As an application, it is proved that the $L^p(\mu)$-boundedness with $p\in(1,\infty)$ of Calderón–Zygmund operators is equivalent to various endpoint estimates.

Keywords

Primary 42B3042B20non-doubling measureRBMO$H^1$-atomic blockCalderón–Zygmund operator
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 1 , February 2008 , pp. 155 - 170
Copyright
Copyright © Edinburgh Mathematical Society 2008