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The higher order commutators of the fractional integrals on Hardy spaces

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  09 April 2009

Shunchao Long  and
Jian Wang
Shunchao Long
Affiliation:
Mathematics DepartmentXiangtan University Xiangtan, 411105 P. R.China e-mail: sclong@xtu.edu.cn, jwang@hnedu.com
Jian Wang
Affiliation:
Mathematics DepartmentXiangtan University Xiangtan, 411105 P. R.China e-mail: sclong@xtu.edu.cn, jwang@hnedu.com
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Abstract

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In this paper we investigate the boundedness on Hardy spaces for the higher order commutator Tb, m generated by the BMO function b and fractional integral type operator Tτ, and establish the boundness theorems for Tτb, m from Hp1.q1.sb, m to Lp2 and to Hp2 (0 < p1 ≤ 1), and from H Ka. p1.sq1, b, m to Ka.p2q2 and to H Ka. p2q2, respectively, for certain ranges of α, p1, q1, p2, q2 and s.

Keywords

Hardy spaceHerz spacecommutatorfractional integral type operatorBMO.

MSC classification

Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B30: $H^p$-spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 1 , August 2005 , pp. 11 - 24
Copyright
Copyright © Australian Mathematical Society 2005

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