Paper Title:

Two Remarks on Commutators of Hardy Operator

Author(s):

Yasuo Komori-Furuya

School of High Technology for Human Welfare 
Tokai University
317 Nishino Numazu, Shizuoka 410-0395 Japan
komori@wing.ncc.u-tokai.ac.jp  

Abstract:

Fu and Lu showed that
the commutator of multiplication operator by b and
the n-dimensional Hardy operator
is bounded on L^p if b is in some CMO space.
We shall prove the converse of this theorem
and also prove that their result is optimal by giving a counterexample

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