A sparse approach to mixed weak type inequalities

In this paper we provide some quantitative mixed weak-type estimates assuming conditions that imply that u v ∈ A ∞ for Calderón–Zygmund operators, rough singular integrals and commutators. The main novelty of this paper lies in the fact that we rely upon sparse domination results, pushing an approach to endpoint estimates that was introduced in Domingo-Salazar et al. (Bull Lond Math Soc 48(1):63–73, 2016) and extended in Lerner et al. (Adv Math 319:153–181, 2017) and Li et al. (J Geom Anal, 2018).