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

Om dit artikel te citeren:

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.