Multiple Weighted Boundedness Of Local Multilinear Hardy-littlewood Maximal Operators

This paper we mainly study the weak boundedness of local multilinear HardyLittlewood maximal operators under the local multiple-weight.First,the definition of local multiple-weight is given and its properties are proved,which generalized the conclusions of local weight and local double-weight.The keys are the construction of the index,and the relationship between the local weight and the local multiple-weight is established.Second,the weak boundedness of local multilinear Hardy-Littlewood maximal operators under the local multiple-weight is proved.The boundedness of the local maximal operator on the local weight and local double-weight is generalized to the local multiple-weight.On the basis of previous studies,this paper enriches the theory of boundedness of local multilinear maximal operator.At the same time,it also played a significant role in the field of harmonic analysis.