Weighted norm estimates of noncommutative Calderón-Zygmund operators

Abstract

This paper is devoted to studying weighted endpoint estimates of operator-valued singular integrals. Our main results include weighted weak-type $(1,1)$ estimate of noncommutative maximal Calderón-Zygmund operators, corresponding version of square functions and a weighted $H_1-L_1$ type inequality. All these results are obtained under the condition that the weight belonging to the Muchenhoupt $A_1$ class and certain regularity assumptions imposed on kernels which are weaker than the Lipschitz condition.

35 pages