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

Jones, Matthew (2015) Compact composition operators with symbol a universal covering map onto a multiply connected domain. Illinois Journal of Mathematics, 59 (3) . pp. 707-715. ISSN 0019-2082

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## 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.

Item Type: Article Volume 59, Number 3, Fall 2015. First available in Project Euclid: 30 September 2016 A. > School of Science and Technology > Design Engineering and Mathematics 19143 Matthew Jones 07 Apr 2016 11:04 05 Jun 2019 21:16 https://eprints.mdx.ac.uk/id/eprint/19143