Local Weighted Boundedness Of Local Hardy-Littlewood Maximal Operator

This paper will study the boundedness of local Hardy-Littlewood maximal operator under the local weight in variable lebesgue space.First,the strong boundedness of local Hardy-Littlewood maximal operator with local weight is proved and promoted the original conclusion.By constracting the w to establish the relationship between the global and local weight functions is the key link of proof.Second,the weak boundedness of local Hardy-Littlewood maximal operator with local weight is proved.The conclusions of this paper further improves the theoretical study of the boundedness of the local maximal operator.At the same time,it also played a significant role in the field of harmonic analysis.