A characterization of Calderón-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 Calderón-Zygmund operators $T:\mathrm{RBMO}(\mu )\to \mathrm{RBMO}(\mu )$ in terms of the function $T1$.

12 pages