数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1338-1346.doi: 10.1016/S0252-9602(10)60129-4

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BOUNDEDNESS OF CALDERÓN-ZYGMUND OPERATORS ON BESOV SPACES AND ITS APPLICATION

杨占英   

  1. Department of Mathematics, South-Central University for Nationalities, Wuhan 430074, China
  • 收稿日期:2008-09-23 出版日期:2010-07-20 发布日期:2010-07-20
  • 基金资助:

    Sponsored by the NSF of South-Central University for Nationalities (YZZ08004) and NNSF of China (10871209)

BOUNDEDNESS OF CALDERÓN-ZYGMUND OPERATORS ON BESOV SPACES AND ITS APPLICATION

 YANG Zhan-Ying   

  1. Department of Mathematics, South-Central University for Nationalities, Wuhan 430074, China
  • Received:2008-09-23 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    Sponsored by the NSF of South-Central University for Nationalities (YZZ08004) and NNSF of China (10871209)

摘要:

In this article, the author introduces a class of non-convolution Calderón-Zygmund operators whose kernels are certain sums involving the products of Meyer wavelets and their convolutions. The boundedness on Besov spaces
Bp0, q(1≤p, q≤ ∞) is also obtained. Moreover, as an application, the author gives a brief proof of the known result that Hörmander condition can ensure the boundedness of convolution-type Calderón-Zygmund operators on Besov spaces Bp0, q(1≤p, q≤ ∞) . However, the proof is quite different from the previous one.

关键词: Calderón-Zygmund operators,  Besov space Meyer wavelet, Hörmander condition

Abstract:

In this article, the author introduces a class of non-convolution Calderón-Zygmund operators whose kernels are certain sums involving the products of Meyer wavelets and their convolutions. The boundedness on Besov spaces
Bp0, q(1≤p, q≤ ∞) is also obtained. Moreover, as an application, the author gives a brief proof of the known result that Hörmander condition can ensure the boundedness of convolution-type Calderón-Zygmund operators on Besov spaces Bp0, q(1≤p, q≤ ∞) . However, the proof is quite different from the previous one.

Key words: Calderón-Zygmund operators,  Besov space Meyer wavelet, Hörmander condition

中图分类号: 

  • 42B20