New York Journal of Mathematics
Volume 24 (2018), 389-403


Hamzeh Keshavarzi and Bahram Khani-Robati

Power bounded composition operators on weighted Dirichlet spaces

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Published: June 30, 2018
Keywords: power bounded, composition operators, weighted Dirichlet space, Riesz operator.
Subject: Primary: 47B33; Secondary: 47B38, 47B06.

In this paper, we study power bounded composition operators Cφ on weighted Dirichlet spaces Dα. As applications, we give the necessary and sufficient conditions for the composition operators to be Riesz operator on Dα, when Cφ is power bounded on Dβ for some β between 0 and α. For α greater than 1, we completely characterize the Riesz composition operators on Dα. Some of the techniques developed in the paper are not new but lead to new results.

Author information

Department of Mathematics, Shiraz University, Shiraz, Iran

Department of Mathematics, Shiraz University, Shiraz, Iran