A Class Of Generalized Calder¨®n-zygmund Operator Commutators Of Boundedness

This thesis contains four chapters, we mainly discuss the boundedness for commutators generated by the Lipschitz function and the generalized Calderon-Zygmund operator and weighted estimates for the multilinear commutators of the generalized Calderon-Zygmund operator.In Chapter 1, we introduce the definition, notation and development of the generalized Calderon-Zygmund operator and its commutators, and put forward the questions to be studied. In Chapter 2, we study the the boundedness for commutators generated by the Lipschitz function and the generalized Calderon-Zygmund operator on the weighted Hardy type spaces. In Chapter 3, We prove that the commutators generated by weighted Lipschitz function and the generalized Calderon-Zygmund operator is bounded from Lp(w) to Lq(w1-q) and from Ln/β(w) to BMO(w). In Chapter 4, we give the weighted (p,p) boundedness and weighted weak type estimates for the multilinear commutators of the generalized Calderon-Zygmund operator.