Weighted mixed endpoint estimates of Fefferman-Stein type for commutators of singular integral operators

Abstract

We deal with mixed weak estimates of Fefferman-Stein type for higher order commutators of Calder\'on-Zygmund operators with BMO symbol. The results obtained are Fefferman-Stein inequalities that include the estimates proved in \cite{BCP22(JMS)} for the case of singular integral operators, as well as the classical weak endpoint estimate for commutators given in \cite{PP01}. We also consider commutators of operators involving less regular kernels satisfying an $L^{\Phi}$--H\"ormander condition. Particularly, the obtained results contain some previous estimates proved in \cite{BCP22(JMS)} and \cite{Lorente-Martell-Perez-Riveros}.