数学物理学报(英文版)

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COMPOSITION OPERATORS ON THE LITTLE BLOCH SPACE IN POLYDISCS

周泽华,朱敏,史济怀   

  1. Department of Mathematics, Tianjin University, Tianjin 300072, China Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
  • 出版日期:2005-10-11 发布日期:2005-10-11
  • 基金资助:

    Supported by the National Natural Science Foundation of China (10371091,
    10001030), and LiuHui Center for Applied Mathematics, Nankai University and Tianjin University

COMPOSITION OPERATORS ON THE LITTLE BLOCH SPACE IN POLYDISCS

 ZHOU Ze-Hua, SHU Min, SHI Ji-Fu   

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

    Supported by the National Natural Science Foundation of China (10371091,
    10001030), and LiuHui Center for Applied Mathematics, Nankai University and Tianjin University

摘要:

Let Un be the unit polydisc of Cn and  = (1, · · · , n) a holomorphic self-
map of Un. This paper shows that the composition operator C induced by  is bounded
on the little Bloch space 0(Un) if and only if l 2 0(Un) for every l = 1, 2, · · · , n,
and also gives a sufficient and necessary condition for the composition operator C to be
compact on the little Bloch space 0(Un).

Abstract:

Let Un be the unit polydisc of Cn and  = (1, · · · , n) a holomorphic self-
map of Un. This paper shows that the composition operator C induced by  is bounded
on the little Bloch space 0(Un) if and only if l 2 0(Un) for every l = 1, 2, · · · , n,
and also gives a sufficient and necessary condition for the composition operator C to be
compact on the little Bloch space 0(Un).

Key words: Little Bloch space, distinguished boundary, composition operator, Bergman metric

中图分类号: 

  • 32A30