Rough Fractional Integral And Its Commutator On Variable Exponents Spaces

In this dissertation,we mainly study the boundedness of rough fractional integral operators and their commutators on several classes of variable exponent Morrey spaces.The main contents are as follows.Firstly,by using the boundedness of the maximal operator with rough kernel in Lp(·)(E)and the boundedness of the variable exponent fractional integral operator from Lp(·)(E)to Lq(·)(E),combined with the method of the hierarchical decomposition of functions and the properties of the generalized variable exponent Morrey space,the boundedness of the maximal operator with rough kernel and variable exponent fractional integral operator on generalized variable exponent Morrey space is proved.Secondly,by the definition of local "complementary" generalized variable exponent Morrey space and BMO space,combined with generalized Holder inequality and function decomposition method,the boundedness of fractional integral operators on local "complementary" generalized variable exponent Morrey spaces is obtained.Finally,by defining the generalized variable exponent Morrey space and using the function decomposition,real variable method and boundedness of variable exponent Lebesgue space,the boundedness of multilinear fractional integral operators on generalized variable exponent Morrey spaces is obtained.