Revisiting mixed weak inequalities of Fefferman-Stein type for commutators of Calderón-Zygmund operators: an improvement

In this paper we establish mixed weak inequalities of Fefferman-Stein type for Calderón-Zygmund operators and their commutators, improving some previous results known in the literature. The main estimates also generalize the classical weighted weak Fefferman-Stein inequalities proved in [19] and [22]. In order to obtain the main results, our approach is to give a strong Fefferman-Stein type inequality for the operators involved with respect to an adequate measure.