数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 292-302.doi: 10.1016/S0252-9602(11)60229-4

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COMPOSITION OPERATORS BETWEEN SOME WEIGHTED HARDY SPACES

徐丽芳1,2|邓方文1   

  1. 1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China 2. Graduate School of the Chinese Academy of Sciences, Beijing 100039, China
  • 收稿日期:2009-09-23 修回日期:2010-04-17 出版日期:2011-01-20 发布日期:2011-01-20
  • 基金资助:

    Supported in part by the National Natural Science Foundation of China (10901158)

COMPOSITION OPERATORS BETWEEN SOME WEIGHTED HARDY SPACES

 XU Li-Fang1,2, DENG Fang-Wen1   

  1. 1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China 2. Graduate School of the Chinese Academy of Sciences, Beijing 100039, China
  • Received:2009-09-23 Revised:2010-04-17 Online:2011-01-20 Published:2011-01-20
  • Supported by:

    Supported in part by the National Natural Science Foundation of China (10901158)

摘要:

Let D be the unit disc and H(D) be the set of all analytic functions on D. In[2], C. Cowen defined a space H = {fH(D) : f(z) =∑k=0ak(z + 1)k, ∀z D, ||f||2 =∑k=0|ak|24k < ∞}. In this article, the authors consider the similar Hardy spaces with arbitrary weights and discuss some properties of them. Boundedness and compactness of composition operators between such spaces are also studied.

关键词: Composition operator, weighted Hardy space

Abstract:

Let D be the unit disc and H(D) be the set of all analytic functions on D. In[2], C. Cowen defined a space H = {fH(D) : f(z) =∑k=0ak(z + 1)k, ∀z D, ||f||2 =∑k=0|ak|24k < ∞}. In this article, the authors consider the similar Hardy spaces with arbitrary weights and discuss some properties of them. Boundedness and compactness of composition operators between such spaces are also studied.

Key words: Composition operator, weighted Hardy space

中图分类号: 

  • 30D55