The High-order Commutator Of Fractional Hardy Operator With Variable Index

In this thesis,we introduced some basic concepts and lemmas of function spaces with variable exponents,and some definitions and properties related to Hardy operators.Then,based on these properties and important lemmas,by using the Jensen and Holder inequali-ties,we established the boundedness of the higher commutators generated by n-dimensional fractional Hardy operators and their conjugate operators of variable order and BMO func-tions on the Herz-Morrey spaces with only one variable exponent.At last,we obtained the boundedness of the higher commutators generated by n-dimensional fractional Hardy operators and their conjugate operators of variable order and Lipschitz functions on the Herz-Morrey spaces with two variable exponents.