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

TL;DR

This paper investigates the product of functions in BMO and H^1 spaces over RD-spaces, extending recent results to a broader class of spaces with reverse doubling properties.

Contribution

It generalizes existing results on BMO and H^1 function products to RD-spaces, a class of spaces with specific geometric and measure-theoretic properties.

Findings

Established new product estimates in RD-spaces.

Extended previous results from Euclidean and metric measure spaces.

Provided a framework for analyzing BMO and H^1 interactions in complex spaces.

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}.