AN INTERPOLATION THEOREM RELATED TO THE HARDY SPACE WITH NON-DOUBLING MEASURE

Abstract

Let $\mu$ be a nonnegative Radon measure satisfying the growth condition that $\mu(B(x,\,r))\leq Cr^{n}$ for any $x\in {\Bbb R}^d$ and $r/gt 0$ and some fixed positive constants $C$ and $n$ with with $0 \lt n\leq d$. Let $H^{1,\,\infty}_{{\rm atb}}(\mu)$ be the Hardy space associated with $\mu$ which was introduced by Tolsa. In this paper, a new interpolation theorems related to $H^{1,\,\infty}_{{\rm atb}}(\mu)$ is established and the interpolation theorem of Tolsa is improved.