Boundedness Of Commutators Of Fractional Integral Operators Related To Differential Operators

In this thesis,we introduced the definition and basic properties of the Morrey-Herz spaces,variable exponent Morrey spaces,variable exponent Herz spaces,the boundedness of fractional integral operators associated with differential operator and its commutator.Then,based on the concepts of space and related theorem properties,by the boundedness of fractional integral operators and their commutators on Lebesgue spaces,using H¨older inequality,we proved that the commutators of fractional integral operators associated with differential operators are bounded on Morrey-Herz spaces,variable exponent Morrey spaces and variable exponent Herz spaces.