数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (2): 243-250.doi: 10.1016/S0252-9602(09)60025-4

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PREDUAL SPACES FOR Q SPACES

彭立中, 杨奇祥   

  1. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
  • 收稿日期:2006-10-29 修回日期:1900-01-01 出版日期:2009-03-20 发布日期:2009-03-20
  • 通讯作者: 彭立中
  • 基金资助:

    Research supported by NNSF of China No.10001027, 90104004,10471002, 973 project of China G1999075105, the innovation funds of Wuhan University, and the subject construction funds of Mathematic and Statistic School, Wuhan University.

PREDUAL SPACES FOR Q SPACES

Peng Lizhong, Yang Qixiang   

  1. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Received:2006-10-29 Revised:1900-01-01 Online:2009-03-20 Published:2009-03-20
  • Contact: Peng Lizhong
  • Supported by:

    Research supported by NNSF of China No.10001027, 90104004,10471002, 973 project of China G1999075105, the innovation funds of Wuhan University, and the subject construction funds of Mathematic and Statistic School, Wuhan University.

摘要:

To find the predual spaces Pα(Rn) of Qα(Rn) is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent atomic characterization of Pα(Rn) is given, then its usual atomic characterization and Poisson extension characterization are given. Finally, the continuity on Pα of Calderón-Zygmund operators is studied, and the result can be also applied to give the Morrey characterization of Pα(Rn).

关键词: Qα space, predual spaces, wavelets, tent atom, usual atom, Poisson extension, Besov spaces, Calderón-Zygmund operator

Abstract:

To find the predual spaces Pα(Rn) of Qα(Rn) is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent atomic characterization of Pα(Rn) is given, then its usual atomic characterization and Poisson extension characterization are given. Finally, the continuity on Pα of Calderón-Zygmund operators is studied, and the result can be also applied to give the Morrey characterization of Pα(Rn).

Key words: Qα space, predual spaces, wavelets, tent atom, usual atom, Poisson extension, Besov spaces, Calderón-Zygmund operator

中图分类号: 

  • 46E15