Boundedness Of Rough Kernel And Fractional Maximal Operators With Variable Kernel

In this dissertation,we shall mainly study the boundedness of maximal operator and fractional maximal operator and its commutator on the weighted ?-central Morrey spaces.The main results are as followsFirstly,by using the weight inequality and other tools,the boundedness of fractional maximal operator and its commutator on the weighted ?-central Morrey spaces are establishedSecondly,by using the estimates of the maximal operator in LP space,we ob-stained the boundedness of the maximal operator with rough kernel on the weighted?-central Morrey spacesFinally,by using the estimates of the fractional maximal operator with variable kernel in Lp spaces,thus,we obtained fractional maximal operator with variable kernel on the weighted ?-central Morrey spaces.