Products of functions in $\BMO$ and $\H^{1}$ spaces on spaces of homogeneous type

Abstract

We give an extension to certain \textit{RD-space} $\X$, i.e space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property, of the definition and various properties of the product of functions in $\BMO(\X)$ and $\H^{1}(\X)$, and functions in Lipschitz space $\Lambda_{\frac{1}{p}-1}(\X)$ and $\H^{p}(\X)$ for $p\in(\frac{\n}{\n+\theta},1]$, where $\n$ and $\theta$ denote respectively the "dimension" and the order of $\X$