<abstract xmlns="http://www.w3.org/1999/xhtml"> Let Φ be an analytic self-map of the open unit disk D in the complex plane. Such a map induces through composition a linear composition operator CΦ : f ↦ f◦Φ.We are interested in the combination of CΦ with the differentiation operator D, that is in the operator DCΦ : f ↦ Φ` · (f ◦ Φ) acting between weighted Bergman spaces and weighted Banach spaces of holomorphic functions </abstract>

Let Φ be an analytic self-map of the open unit disk D in the complex plane. Such a map induces through composition a linear composition operator CΦ : f ↦ f◦Φ.We are interested in the combination of CΦ with the differentiation operator D, that is in the operator DCΦ : f ↦ Φ` · (f ◦ Φ) acting between weighted Bergman spaces and weighted Banach spaces of holomorphic functions

Composition followed by differentiation between weighted Bergman spaces and weighted Banach spaces of holomorphic functions

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Let Φ be an analytic self-map of the open unit disk D in the complex plane. Such a map induces through composition a linear composition operator CΦ : f ↦...

Composition followed by differentiation between weighted Bergman spaces and weighted Banach spaces of holomorphic functions

Published Online: Nov 05, 2014

Page range: 107 - 116

Received: Oct 07, 2013

DOI: https://doi.org/10.2478/ausm-2014-0021

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.