数学物理学报(英文版) ›› 2005, Vol. 25 ›› Issue (1): 137-144.

• 论文 • 上一篇    下一篇

COMMUTATORS OF SINGULAR INTEGRAL OPERATORS WITH NON-SMOOTH KERNELS

邓东臯,颜立新   

  1. Department of Mathematics, Zhongshan University
  • 出版日期:2005-01-20 发布日期:2005-01-20
  • 基金资助:

    Project supported by NSF of China (1017111, 10371134)
    and the Foundation of Advanced Research Center, Zhongshan University.

COMMUTATORS OF SINGULAR INTEGRAL OPERATORS WITH NON-SMOOTH KERNELS

 DENG Dong-Gao, YA Li-Xin   

  1. Department of Mathematics, Zhongshan University
  • Online:2005-01-20 Published:2005-01-20
  • Supported by:

    Project supported by NSF of China (1017111, 10371134)
    and the Foundation of Advanced Research Center, Zhongshan University.

摘要:

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.

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

中图分类号: 

  • 42B20