The Variable Index Fractional Integral Commutator On The Variable Index Space

In this thesis,we introduced the definitions and basic properties of the variable fractional integral operators and its commutators.Then,by the boundedness of variable fractional integral operators on Morrey spaces with variable exponents,using the properties of Lipschitz functions,the boundedness of the commutators generated by variable fractional integral operators and Lipschitz functions is obtained.Finally,based on the atomic decomposition of Herz-Hardy spaces with variable exponents,we discussed the boundedness of variable fractional integral operators with homogeneous kernel and its commutators on the Herz-Hardy spaces with variable exponents.