COMMUTATORS OF SINGULAR INTEGRAL OPERATORS WITH NON-SMOOTH KERNELS

Abstract

Abstract:

Let $T$ be a singular integral operator
bounded on $L^p({{\bf R}^n})$ for some $p$ , $1 The authors give
a sufficient condition on the kernel of
$T$ so that when $b\in$ BMO, the commutator
$[b, T](f)=T(b f)-b T(f)$ is bounded on the space $L^p$ for all $p, 1 The condition of this paper is weaker than the usual pointwise
H\"ormander condition.

Key words: Commutator, BMO;singular integrals;semigroup kernel

CLC Number:

42B20

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DENG Dong-Gao, YA Li-Xin. COMMUTATORS OF SINGULAR INTEGRAL OPERATORS WITH NON-SMOOTH KERNELS[J].Acta mathematica scientia,Series B, 2005, 25(1): 137-144.

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