Noncommutative weak type $(1,1)$ estimates for Calderón-Zygmund operators with a class of $L_1$-integral conditions

Abstract

We construct a slightly new noncommutative Calderón-Zygmund decomposition by further splitting the bad function. Using this tool, we prove the weak type (1,1) boundedness of noncommutative Calderón-Zygmund operators under a class of $L_1$-integral conditions, which are close to $L_1$-Dini conditions.