Weighted composition operators acting on Dirichlet type spaces

Authors

  • Sepideh Nasresfahani
  • Hamid Vaezi

DOI:

https://doi.org/10.30495/jme.v14i0.995

Keywords:

Weighted composition operator, Dirichlet type spaces, Boundedness, Carleson measure, ISometry.

Abstract

In this paper we study the weighted composition operator $\psi C_\phi$ on the Dirichlet type spaces $\mathit{D}^p_\alpha(\mathbb{D})$. We show tht if theweighted composion operator $\psi C_\phi$ is bounded on such spaces (for 1\leq p<2$ then the related measure $\mu_{p,\alpha,\psi}$ is a Carleson measure. Also we show that if the weighted composition operator $\psi C_\phi$ is an isomety on $\mathit{D}^p_\alpha(\mathbb{D})$ then $\psi.\phi$ is a rotation map on $\mathbb{D}$.

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Published

2019-04-10

Issue

Vol. 14

Section

Vol. 14, No. 2, (2020)

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