Acta mathematica scientia,Series B ›› 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

 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)

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

CLC Number: 

  • 30D55
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