On the product of functions in $BMO$ and $H^1$ over spaces of homogeneous type

Abstract

Let $\mathcal{X}$ be an RD-space, which means that $\mathcal{X}$ is a space of homogeneous type in the sense of Coifman-Weiss with the additional property that a reverse doubling property holds in $\mathcal{X}$. The aim of the present paper is to study the product of functions in $BMO$ and $H^1$ in this setting. Our results generalize some recent results in \cite{Feu} and \cite{LP}.

J. Math. Anal. Appl. (to appear)