A characterization of Calderón–Zygmund operators on the regular $\mathrm{BMO}$ space

Let $\mathrm{RBMO}(\mu) = \mathrm{RBMO}(\mathbb{R}^m, \mu)$ denote the regular $\mathrm{BMO}$ space introduced by X. Tolsa for an $n$-dimensional 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 $T1$.