Boundedness Of Maximal Operator On Local Morrey Spaces

In this article,we mainly study the boundedness of local maximal operator in local Morrey spaces in the sense of local weight.Firstly,we study some properties of A_p,locweight on a non empty open set(?).Secondly,the strong boundedness of locally weighted maximal operator in the sense of local weight are proved.Finally,the local Hardy-Littlewood maximal operator is controlled by the local weighted maximal operator,and the local covering lemma is applied to obtain the weighted boundedness of the local Hardy-Littlewood maximal operator in local Morrey spaces.