变指标分数次Hardy算子的高阶交换子

Higher Order Commutators of Fractional Hardy Operators with Variable Index

基于Hardy算子与BMO函数的性质及变指数Herz-Morrey空间的定义,运用H9lder不等式等估计,建立变指标的分数次Hardy算子与BMO函数生成的高阶交换子在变指数Herz-Morrey空间上的有界性,从而将经典分数次Hardy算子高阶交换子的有界性推广到变指标分数次Hardy算子的高阶交换子上,当变指数β(x)恒为常数时,变指标分数次Hardy算子即为经典的分数次Hardy算子.

Based on the properties of Hardy operators and BMO functions, together with the definition of Herz-Morrey spaces with variable exponent, and by using the H61der inequalities, we established the boundedness of the higher order commutators generated by fractional Hardy operators with variable index and BMO functions on the Herz-Morrey spaces with variable exponent. The result generalized the boundedness of the higher order commutators of the classical fractional Hardy operators to the higher order commutators of fractional Hardy operators with variable index. When the variable exponentβ（x） was a constant, the fractional Hardy operators were the classical fractional Hardy operators.