Some Estimates For The Multilinear Operators And Its Commutators

There are three chapters in this dissertation, which focuses on three con-tents: the boundedness of commutators generated by the multilinear Caldero′n-Zygmund integral operators and BMO(Rn) functions on the product Herz typespaces, which contains Herz space, Herz-Hardy spaces and Herz-Morrey spaces;we also studied the weighted boundedness of this commutator.The outline of the paper is arranged as follows:The purpose of Chapter1 is devoted to study the boundedness of multilinearCaldero′n-Zygmund integral operator on the product Herz-Morrey spaces.In Chapter 2 we proceed to investigate the boundedness of commutator gen-erated by multilinear Calder′on-Zygmund integral operator and BMO(Rn) func-tions on the product Herz type spaces, which contains Herz space and Herz-Hardyspaces, specially, we get the power weight boundedness.The purpose of chapter 3 is devoted to study the weighted estimate of thecommutator generated by multilinear Caldero′n-Zygmund integral operator andBMO(Rn) functions.The results of us can be seen as the natural extension of classical Calder′on-Zygmund operator theory to the vector space. And some methods in this disser-tation are di?erent from the classical case and the estimates we need are moresubtle.