Bulletin de la Société Royale des Sciences de Liège

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Elke Wolf

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

(Volume 83 - Année 2014 — Articles)
Article
Open Access

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 : http://popups.ulg.be/0037-9565/index.php?id=4313.

About: Elke Wolf

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