A characterization of Calder\'on-Zygmund operators on RBMO

Abstract

Let $\mathrm{RBMO}(\mu) = \mathrm{RBMO}(\mathbb{R}^m, \mu)$ denote the regular BMO space introduced by X. Tolsa for an $n$-dimensional finite positive measure on $\mathbb{R}^m$, $0<n \le m$. We characterize the bounded Calder\'on-Zygmund operators $T:\mathrm{RBMO}(\mu) \to \mathrm{RBMO}(\mu)$ in terms of the function $T1$.