数学物理学报(英文版)

• 论文 • 上一篇    

COMPOSITION OPERATORS ON ANALYTIC VECTOR-VALUED NEVANLINNA CLASSES

 王茂发   

  1. Wuhan Institute of Physics and Mathematics, CAS, Wuhan 430071, China
    School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 出版日期:2005-10-11 发布日期:2005-10-11
  • 基金资助:

    This research is supported by the NNSF of China (10401027; 10371093).

COMPOSITION OPERATORS ON ANALYTIC VECTOR-VALUED NEVANLINNA CLASSES

Wang Maofa   

  • Online:2005-10-11 Published:2005-10-11
  • Supported by:

    This research is supported by the NNSF of China (10401027; 10371093).

摘要:

Let ' be an analytic self-map of the complex unit disk and X a Banach space.
This paper studies the action of composition operator C' : f → f ? ' on the vector-valued
Nevanlinna classes N(X) and Na(X). Certain criteria for such operators to be weakly
compact are given. As a consequence, this paper shows that the composition operator
C' is weakly compact on N(X) and Na(X) if and only if it is weakly compact on the
vector-valued Hardy space H1(X) and Bergman space B1(X) respectively.

Abstract:

Let ' be an analytic self-map of the complex unit disk and X a Banach space.
This paper studies the action of composition operator C' : f → f ? ' on the vector-valued
Nevanlinna classes N(X) and Na(X). Certain criteria for such operators to be weakly
compact are given. As a consequence, this paper shows that the composition operator
C' is weakly compact on N(X) and Na(X) if and only if it is weakly compact on the
vector-valued Hardy space H1(X) and Bergman space B1(X) respectively.

Key words: Composition operator, boundedness, weak compactness, Carleson measure,
vector-valued Nevanlinna class

中图分类号: 

  • 47B38 46E15