J. Aust. Math. Soc.  79 (2005), 11-24
The higher order commutators of the fractional integrals on Hardy spaces

 Shunchao Long   Mathematics Department   Xiangtan University   Xiangtan, 411105   P. R. China  sclong@xtu.edu.cn
 and
 Jian Wang   Mathematics Department   Xiangtan University   Xiangtan, 411105   P. R. China  jwang@hnedu.com

Abstract
In this paper we investigate the boundedness on Hardy spaces for the higher order commutator generated by the BMO function b and fractional integral type operator , and establish the boundedness theorems for from to and to  , and from to and to , respectively, for certain ranges of , , , , and .