Weighted Estimates For Toeplitz Operator Related To Singular Integral Operators

In this paper, we study the weighted estimates for Toeplitz operator related to singular integraloperators. This paper is constituted with four chapters.In chapter1, we introduce the background, the main definitions and the main results of thispaper.In chapter2, we study the two weighted estimates for commutator of strongly singular integraloperator. The commutator is generalized by BMO(ω) function b and strong Caldero′n-Zygmundoperator T.In chapter3, we study the weighted estimates for the Toeplitz operator Tbrelated to stronglysingular integral operator and the weighted Lipschitz function. On the other hand, we also studythe weighted estimates for the Toeplitz operator Tbrelated to strongly singular integral operatorand the weighted BMO function.In chapter4, we study the weighted estimates for the Toeplitz operator Tbrelated to singularintegral operator with non-smooth kernel and the weighted Lipschitz function. On the other hand,we also study the weighted estimates for the Toeplitz operator Tbrelated to singular integraloperator with non-smooth kernel and the weighted BMO function.