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

Jones, Matthew ORCID logoORCID: https://orcid.org/0000-0002-5252-5234 (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 [Article]

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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
Additional Information: Volume 59, Number 3, Fall 2015.
First available in Project Euclid: 30 September 2016
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 19143
Useful Links:
Depositing User: Matthew Jones
Date Deposited: 07 Apr 2016 11:04
Last Modified: 23 Jun 2022 05:06
URI: https://eprints.mdx.ac.uk/id/eprint/19143

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