Weighted norm inequalities for Toeplitz type operators associated to generalized Calderón–Zygmund operators

摘要

Let T1 be a generalized Calderón–Zygmund operator or ±I ( the identity operator), let T2 and T3 be the linear operators, and let T3 = ±I. Denote the Toeplitz type operator by T^b = T1M^bIαT2 + T3IαM^bT4, where M^bf = bf,  and Iα is fractional integral operator. In this paper, we establish the sharp maximal function estimates for T^b when b belongs to weighted Lipschitz function space, and the weighted norm inequalities of T^b on weighted Lebesgue space are obtained.