数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1145-1156.doi: 10.1016/S0252-9602(14)60075-8

• 论文 • 上一篇    下一篇

AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES

陈志华1|江良美2|颜启明1*   

  1. 1. Department of Mathematics, Tongji University, Shanghai 200092, China;
    2. Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, China
  • 收稿日期:2013-04-02 出版日期:2014-07-20 发布日期:2014-07-20
  • 通讯作者: 颜启明,qiming@hotmail.com E-mail:zzzhhc@tongji.edu.cn; liangying1231@163.com; yan qiming@hotmail.com
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (11171255, 11101279) and the Natural Science Foundation of Shanghai (13ZR1444100).

AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES

 CHEN Zhi-Hua1, JIANG Liang-Mei2, YAN Qi-Ming1*   

  1. 1. Department of Mathematics, Tongji University, Shanghai 200092, China;
    2. Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, China
  • Received:2013-04-02 Online:2014-07-20 Published:2014-07-20
  • Contact: YAN Qi-Ming,qiming@hotmail.com E-mail:zzzhhc@tongji.edu.cn; liangying1231@163.com; yan qiming@hotmail.com
  • Supported by:

    Project supported by the National Natural Science Foundation of China (11171255, 11101279) and the Natural Science Foundation of Shanghai (13ZR1444100).

摘要:

In this paper, we define the generalized counting functions in the higher dimen-sional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to be bounded or compact is also given.

关键词: essential norm, composition operator, weighted Bergman space

Abstract:

In this paper, we define the generalized counting functions in the higher dimen-sional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to be bounded or compact is also given.

Key words: essential norm, composition operator, weighted Bergman space

中图分类号: 

  • 47B38