Local Weighted Boundedness Of Fractional Maximal Operators In Variable Lebesgue Spaces

The paper mainly study the problem of local weighted boundedness of fractional maximal operators in variable Lebesgue spaces.In this paper,we first introduce the development history of variable Lebesgue spaces?maximal operators and Ap weights.At the same time,we introduce the con-clusion about the boundedness of fractional maximal operators in variable Lebesgue spaces.Then,we give the definition of local Ap(·),q(·)weights in variable Lebesgue spaces and prove their properties,the local weighted boundedness of fractional max-imal operators is proved.In this paper,the definition of local Ap(·),q(·)weights and local fractional maxi-mal operators in variable Lebesgue spaces are given for the first time,The conclusion of this paper further improves the weighted boundedness of fractional maximal op-erators.