Compact composition operators with symbol a universal covering map onto a multiply connected domain

Article

Jones, M. 2015. Compact composition operators with symbol a universal covering map onto a multiply connected domain. Illinois Journal of Mathematics. 59 (3), pp. 707-715.
TypeArticle
TitleCompact composition operators with symbol a universal covering map onto a multiply connected domain
AuthorsJones, M.
Abstract

We generalise previous results of the author concerning the compactness of composition operators on the Hardy spaces $H^p$, $1\leq p<\infty$, whose symbol is a universal covering map from the unit disk in the complex plane to general finitely connected domains. We demonstrate that the angular derivative criterion for univalent symbols extends to this more general case. We further show that compactness in this setting is equivalent to compactness of the composition operator induced by a univalent mapping onto the interior of the outer boundary component of the multiply connected domain.

PublisherIllinois University
JournalIllinois Journal of Mathematics
ISSN0019-2082
Publication dates
Print2015
Online30 Sep 2016
Publication process dates
Deposited07 Apr 2016
Accepted16 Mar 2016
Output statusPublished
Accepted author manuscript
Additional information

Volume 59, Number 3, Fall 2015.
First available in Project Euclid: 30 September 2016

Web address (URL)http://projecteuclid.org/euclid.ijm/1475266405
LanguageEnglish
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