IJPAM: Volume 7, No. 3 (2003)

NOTES ON COMMUTATORS OF HARDY OPERATORS

Yasuo Komori
School of High Technology for Human Welfare
Tokai University
Nishino 317, Numazu, Shizuoka 410-0395, JAPAN
e-mail: komori@wing.ncc.u-tokai.ac.jp


Abstract.Shunchao and Jian showed that the commutator of multiplication operator by $b$ and Hardy operator is bounded on $L^p$ if $b$ is in one sided dyadic $CMO^p$. We prove the converse of this theorem.

Received: May 13, 2003

AMS Subject Classification: 46E15

Key Words and Phrases: Hardy operator, commutator, one sided dyadic $CMO$

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 7
Issue: 3