n维分数次Hausdorff高阶交换子的有界性

Boundedness of Higher Order Commutators of n-Dimensional Fractional Hausdorff Operators

通过定义n维分数次Hausdorff算子HlΦ,利用CMO函数和Lipschitz函数的John-Nirenberg型不等式,分别得到了由HlΦ和CMO及Lipschitz函数生成的高阶交换子Hl,mΦ,b在Lebesgue空间、Herz空间和Morrey-Herz空间上的有界性结果.

The n-dimensional fractional Hausdorff operators HOιφ were defined. With the aid of John- Nirenberg inequalities about the CMO and Lipschitz functions, the boundedness of higher order commutators generated by HOιφ and CMO or Lipschitz functxons HOιφ,mb was established on Lebesgue spaces, Herz spaces, and Morrey-Herz spaces respectively.