The Boundedness For Dini Type Of Multilinear Operators

This paper is divided into four sections.We mainly study the boundedness of Dini type multilinear operators and commutators generated by Dini type multilinear operators,Lipschitz functions and BMO functions on several kinds of function spaces.The definition of the multilinear Calderon-Zygmund operators with Dini kernel as follows:T(f1,f2…,fm)=?(R~n)mk(x,y1,y2,…,ym)f1(y1)f2(y2)…fm(ym)dy1…dym.Call it T:?(R~n)×?(R~n)×…×?(R~n)??(R~n)is a linear Calderon-Zygmund operator of w(t)type..(?) and (?).Chapter 1:The author describes the research background,research status and main results of multilinear operators.Chapter 2:The author obtains the boundedness of Dini type multilinear operators on Herz type Hardy spaces by means of the ring decomposition and the eigendecomposition of the central atom.Chapter 3:The author uses the sharp maximum function method to estimate and prove the boundedness of the commutator and iterative commutator generated by the Dini-type multilinear Calderon-Zygmund operators and the Lipschitz function on the weighted Lebesgue space.Among them,the multilinear commutator and iterative commutator are defined as:Suppose T is a multilinear Calderon-Zygmund operator,(?)=(b1,…,bm)?Lip?m,j=1,…,m defined on R~n and locally integrable,multilinear commutator is defined as (?),among them Let (?)=(b1,…,bm),b1,i=1,…,m be defined on R~n and locally integrable,and the iterative commutator is defined as (?)Chapter 4:The author uese the properties of the weight function to prove that the Lipschitz function,the BMO function and the commutator generated by the Dini type multilinear operator are bounded on the weighted Morrey-Herz space.