Weighted Norm Inequalities for Toeplitz Type Operator Related to Singular Integral Operator with Variable Kernel

Let Tk,1 be the singular integrals with variable Calderón-Zygmund kernels or ±Ⅰ(the identity operator), let Tk,2 and Tk,4 be the linear operators, and let Tk,3= ±Ⅰ.Denote the Toeplitz type operator by ■ where Mbf = bf, and Ⅰα is the fractional integral operator. In this paper, we investigate the boundedness of the operator on weighted Lebesgue space when b belongs to weighted Lipschitz space.