Isometric composition operators on weighted Dirichlet-type spaces

In this article, we characterize the surjective isometric composition operator C φ on the weighted Dirichlet-type spaces of the unit disk D , where φ is an analytic self-map of D , and show that C φ is a surjective isometry if and only if φ is a rotation map. 2000 MSC : Primary: 47B33; Secondary: 30...

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Bibliographic Details
Published in:Journal of inequalities and applications 2012-02, Vol.2012 (1), p.1-23, Article 23
Main Authors: Geng, Li-Gang, Zhou, Ze-Hua, Dong, Xing-Tang
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:In this article, we characterize the surjective isometric composition operator C φ on the weighted Dirichlet-type spaces of the unit disk D , where φ is an analytic self-map of D , and show that C φ is a surjective isometry if and only if φ is a rotation map. 2000 MSC : Primary: 47B33; Secondary: 30D45; 30H30; 30H05; 47B38.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/1029-242X-2012-23