Weighted Estimation For Some Operators In Herz-Morrey Spaces With Variable Exponent

This dissertation mainly studies the boundedness of several kinds of operators on the weighted Lebesgue space with variable exponent and the weighted Herz-Morrey spaces with variable exponent.The main results are as follows.First of all,we proved the boundedness of the Marcinkiewicz integral operator with variable kernel ?? onLp(·)(?)and the boundedness of the Marcinkiewicz in-tegral operator with variable kernel ?? on the weighted Herz-Morrey spaces with variable exponent MKq,p(·)?,?(?).Secondly,by using the boundedness of fractional integral operator with rough kernel T?,lf(x)on the weighted Lebesgue spaces with variable exponent,the bound-edness of fractional integral operator with rough kernel T?,lf(x)on the weighted Herz-Morrey spaces with variable exponent is obtained.Finally,we obtain the boundedness of the fractional integral operator with variable index Il(·)f(x)and its commutator[b,Il(·)]on the weighted Herz-Morrey spaces with variable exponent.