The Local Weighted Boundedness Of The Local Multilinear Operator

As is known to all,the boundedness of the operator in different space,is a indis?pensable process in the field of harmonic analysis,multilinear operators theory and the theory of loeal weights toward harmonic analysis,Equivalent to cells and bodies,they all have important position.This article mainly studied the strong bounded-ness of local multilinear Hardy-Littlewood operators under the local multiple-weight on measure metric spaces.Firstly,the development history of harmonie analysis is briefly described,the boundedness of maximal operators and the relevant conclusions of weighted bound-edness are emphatically introduced,and then such factors as the multilinear and local are integrated into the theoretical system of maximal operators.Secondly,combination of local weight,based on the boundedness of the weight-ed local multilinear operators,we started the research on local multilinear Hardy-Littlewood operators under the local multiple-weight in measure metric spaces.Mainly discusses it's strong boundedness,therewith given several remarks about Ap?,p,expanded relevant conclusions of classical multiple-weight.Finally,On the basis of the existing research,the power bump condition and condition(A)is defined which is stronger than AAp?,p condition and weaker than A?,?condition,respectively.And we proved that the multilinear maximal operators in the measure metric space satisfy the weak weighted boundedness with the power bump condition.These works help us to find the connection between classical multiple-weight and local multiple-weight.The conclusions of this paper makes us have a deeper understanding for the local nmltilineax maximal operators.At the same time,it also deepens our under-standing of this subject,and it make a little contribution to the research work on the subject of Harmonic analysis.