Abstract:

The n-dimensional fractional Hausdorff operators H^l_Φ were defined. With the aid of  JohnNirenberg inequalities about the CMO and Lipschitz functions, the boundedness of higher order commutators generated by H^l_Φ and CMO  or Lipschitz functions H^l,m_Φ,b was established on Lebesgue spaces, Herz spaces, and MorreyHerz spaces respectively.

Key words: n-dimensional fractional Hausdorff operator, Lipschitz functions, CMO functions, commutators