Compact T(1) theorem à la Stein

Abstract

We prove a compact $T\left(1\right)$ theorem, involving quantitative estimates, analogous to the quantitative classical $T\left(1\right)$ theorem due to Stein. We also discuss the $C_c^{\infty }$-to-CMO mapping properties of non-compact Calderón-Zygmund operators as well as the sequential completeness properties of some subspaces of BMO under different topologies.