数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (2): 425-438.doi: 10.1016/S0252-9602(17)30012-7

• 论文 • 上一篇    下一篇

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

黎深莲, 张学军, 徐思   

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha 410006, China
  • 收稿日期:2015-09-02 出版日期:2017-04-25 发布日期:2017-04-25
  • 通讯作者: Xuejun ZHANG,E-mail:xuejunttt@263.net E-mail:xuejunttt@263.net
  • 作者简介:Xuejun ZHANG,E-mail:xuejunttt@263.net
  • 基金资助:

    The research is supported by the National Natural Science Foundation of China (11571104) and Hunan Provincial Natural Science Foundation of China (2015JJ2095)

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

Shenlian LI, Xuejun ZHANG, Si XU   

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha 410006, China
  • Received:2015-09-02 Online:2017-04-25 Published:2017-04-25
  • Contact: Xuejun ZHANG,E-mail:xuejunttt@263.net E-mail:xuejunttt@263.net
  • Supported by:

    The research is supported by the National Natural Science Foundation of China (11571104) and Hunan Provincial Natural Science Foundation of China (2015JJ2095)

摘要:

Let p > 0 and μ be a normal function on[0,1), ν(r)=(1-r2)1+(n/p) μ(r) for r ∈[0,1). In this article, the bounded or compact weighted composition operator Tφ,ψ from the μ-Bergman space Ap(μ) to the normal weight Bloch type space βν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator Cφ is compact from Ap(μ) to βν is given. At the same time, the authors give the briefly sufficient and necessary condition that Cφ is compact on βu for a > 1.

关键词: u-Bergman space, u-Bloch space, composition operator, compactness

Abstract:

Let p > 0 and μ be a normal function on[0,1), ν(r)=(1-r2)1+(n/p) μ(r) for r ∈[0,1). In this article, the bounded or compact weighted composition operator Tφ,ψ from the μ-Bergman space Ap(μ) to the normal weight Bloch type space βν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator Cφ is compact from Ap(μ) to βν is given. At the same time, the authors give the briefly sufficient and necessary condition that Cφ is compact on βu for a > 1.

Key words: u-Bergman space, u-Bloch space, composition operator, compactness