A characterization of Calderón–Zygmund operators on the regular BMO space

Let R B M O ( μ ) = R B M O ( R m , μ ) RBMO(μ ) = RBMO(R^m,μ ) denote the regular BMO space introduced by X. Tolsa for an n n -dimensional finite positive measure on R m R^m , 0 > n ≤ m 0\!>n\!≤ \!m . We characterize the bounded Calderón–Zygmund operators T : R B M O ( μ ) → R B M O ( μ ) T RBMO(μ )→ RBMO(μ ) in terms of the function T 1 T1 .