On weighted composition operators acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces

Elke Wolf¹

¹ Institut für Mathematik Universität Paderborn Warburger Str. 100 D-33098 Paderborn, Germany

Annales Polonici Mathematici, Tome 101 (2011) no. 1, pp. 21-29

Résumé

Let $\phi: \mathbb{D} \to \mathbb{D}$ and $\psi: \mathbb{D} \to \mathbb{C}$ be analytic maps. They induce a weighted composition operator $\psi C_{\phi}$ acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions $\psi$ and $\phi$

Détail

DOI : 10.4064/ap101-1-2

Keywords: phi mathbb mathbb psi mathbb mathbb analytic maps induce weighted composition operator psi phi acting between weighted bergman spaces infinite order weighted bloch type spaces under assumptions weights characterization operator bounded terms weights involved functions psi phi