The Boundedness Of A Class Of Multilinear Operators And Their Commutators

In the recent paper, we study the boundedness of a class of multilinear operators and theircommutators. The paper is constituted with six chapters.In chapter1, we introduce the background and main results about m-linear singular integraloperator and other operators associated with it. Besides, we also simply illustrate how and whythis topics comes out.In chapter2, we present two weighted BMO estimates for the commutators of the maximalmultilinear operator. The commutators are T_Σb and T_Πb.In chapter3, we consider the weighted Lipschitz estimates for the commutators of the maximalmultilinear operator. The commutators are T_Σb and T_Πb.In chapter4, we discuss the multiple weighted estimates for vector-valued maximal multilinearoperator and its commutator.In chapter5, we introduce the knowledge and results about the Hardy space, and then brieflyconsider the weak boundedness of the iterated commutators of m-linear Caldero′n-Zygmund oper-ator as well as the maximal multilinear operator on the product of Hardy spaces.In chapter6, we discuss the multiple weighted estimates for the vector-valued multilinearoperator with non-smooth kernels and its commutators.