A characterization of Calderón-Zygmund operators on RBMO

Let $\mathrm{R}\mathrm{B}\mathrm{M}\mathrm{O}(\mu )=\mathrm{R}\mathrm{B}\mathrm{M}\mathrm{O}({\mathbb{R}}^m,\mu )$ 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 $T:\mathrm{R}\mathrm{B}\mathrm{M}\mathrm{O}(\mu )\to \mathrm{R}\mathrm{B}\mathrm{M}\mathrm{O}(\mu )$ in terms of the function $T1$.