J. Aust. Math. Soc.  79 (2005), 149-182
Local hardy and BMO spaces on non-homogeneous spaces

Dachun Yang
  School of Mathematical Sciences
  Beijing Normal University
  Beijing 100875
  People's Republic of China

Let $\mu$ be a Radon measure on $\mathbb{R}^d$ which may be non doubling. The only condition that $\mu$ must satisfy is the size condition $\mu(B(x,r))\le Cr^n$ for some fixed $n\in(0,d]$. Recently, Tolsa introduced the spaces $RBMO(\mu)$ and $H^{1,\infty}_{atb}(\mu)$, which, in some ways, play the role of the classical spaces $BMO$ and $H^1$ in case $\mu$ is a doubling measure. In this paper, the author considers the local versions of the spaces $RBMO(\mu)$ and $H^{1,\infty}_{atb}(\mu)$ in the sense of Goldberg and establishes the connections between the spaces $RBMO(\mu)$ and $H^{1,\infty}_{atb}(\mu)$ with their local versions. An interpolation result of linear operators is also given.
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