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Proceedings of the Edinburgh Mathematical Society (1)

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A NEW CHARACTERIZATION FOR REGULAR BMO WITH NON-DOUBLING MEASURES
Guoen Hu, Xin Wang, Dachun Yang
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 51 / Issue 1 / February 2008

Published online by Cambridge University Press:

04 February 2008, pp. 155-170
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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.