Bulletin de la Société Royale des Sciences de Liège Bulletin de la Société Royale des Sciences de Liège -  Volume 83 - Année 2014  Articles 

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

Elke Wolf, 
Mathematical Institute, University of Paderborn, D-33095 Paderborn, Germany, lichte@math.uni-paderborn.de

Abstract

Let ϕ be an analytic self-map of the open unit disk in the complex plane. Such a map induces through composition a linear composition operator Cϕ: f|→foϕ. We are interested in the combination of Cϕwith the differentiation operator D, that is in the operator DCϕ: f|→ϕ′ (f′oϕ) acting between weighted Bergman spaces and weighted Banach spaces of holomorphic functions.

1MSC 2010: 47B33, 47B38

To cite this article

Elke Wolf, «Composition followed by differentiation between weighted Bergman spaces and weighted Banach spaces of holomorphic functions», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 83 - Année 2014, Articles, 49 – 55 URL : https://popups.uliege.be/0037-9565/index.php?id=4313.