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Czechoslovak Mathematical Journal

, Volume 66, Issue 1, pp 27–34 | Cite as

Isometric composition operators on weighted Dirichlet space

  • Shi-An Han
  • Ze-Hua Zhou
Article

Abstract

We investigate isometric composition operators on the weighted Dirichlet space \({D_\alpha }\) with standard weights \({(1 - {\left| z \right|^2})^\alpha },\alpha > - 1\). The main technique used comes from Martín and Vukotić who completely characterized the isometric composition operators on the classical Dirichlet space D. We solve some of these but not in general. We also investigate the situation when \({D_\alpha }\) is equipped with another equivalent norm.

Keywords

composition operator weighted Dirichlet space isometry 

MSC 2010

46B04 47B38 47B33 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016

Authors and Affiliations

  1. 1.Department of MathematicsTianjin UniversityJinnan, TianjinP.R. China
  2. 2.Department of MathematicsTianjin UniversityJinnan, TianjinP.R. China

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