数学物理学报(英文版) ›› 2005, Vol. 25 ›› Issue (3): 545-554.

• 论文 • 上一篇    下一篇

ON THE COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

胡国恩   

  1. Department of Applied Mathematics, University of Information Engineering,
    P. O. Box 1001-747, Zhengzhou 450002, China
  • 出版日期:2005-07-20 发布日期:2005-07-20
  • 基金资助:

    This research was supported by the NNSF of China (10271015)

ON THE COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

 HU Guo-En   

  • Online:2005-07-20 Published:2005-07-20
  • Supported by:

    This research was supported by the NNSF of China (10271015)

摘要:

Lp(Rn) (1 < p < 1) boundedness and a weak type endpoint estimate are
considered for the commutators of singular integral operators. A condition on the associated
kernel is given under which the L2(Rn) boundedness of the singular integral operators
implies the Lp(Rn) boundedness (1 < p < 1) and the weak type (H1(Rn), L1(Rn))
boundedness for the corresponding commutators. A new interpolation theorem is also
established.

Abstract:

Lp(Rn) (1 < p < 1) boundedness and a weak type endpoint estimate are
considered for the commutators of singular integral operators. A condition on the associated
kernel is given under which the L2(Rn) boundedness of the singular integral operators
implies the Lp(Rn) boundedness (1 < p < 1) and the weak type (H1(Rn), L1(Rn))
boundedness for the corresponding commutators. A new interpolation theorem is also
established.

Key words: Commutator;singular integral operators;BMO(Rn), interpolation

中图分类号: 

  • 42B20