Calder\'on-Zygmund operators on RBMO

TL;DR

This paper establishes a new sufficient condition for the boundedness of Calderón-Zygmund operators on the RBMO space associated with a finite positive measure, advancing the understanding of singular integral operators in non-doubling measure contexts.

Contribution

It introduces a $T1$ condition that guarantees boundedness of Calderón-Zygmund operators on RBMO, extending classical results to more general measures.

Findings

Proves a $T1$ condition for boundedness on RBMO.

Extends Calderón-Zygmund theory to non-doubling measures.

Provides new tools for analysis on irregular measure spaces.

Abstract

Let $\mu$ be an $n$-dimensional finite positive measure on $\mathbb{R}^m$. We obtain a $T1$ condition sufficient for the boundedness of Calder\'{o}n-Zygmund operators on $\textrm{RBMO}(\mu)$, the regular BMO space of Tolsa.