Compact composition operators with symbol a universal covering map

Article

Jones, M. 2015. Compact composition operators with symbol a universal covering map. Journal of Functional Analysis. 268 (4), pp. 887-901. https://doi.org/10.1016/j.jfa.2014.11.003
TypeArticle
TitleCompact composition operators with symbol a universal covering map
AuthorsJones, M.
Abstract

In this paper we study composition operators, Cϕ, acting on the Hardy spaces that have symbol, ϕ , a universal covering map of the disk onto a finitely connected domain of the form D0\{p1,…,pn}, where D0 is simply connected and pi, i=1,…,ni=1,…,n, are distinct points in the interior of D0. We consider, in particular, conditions that determine compactness of such operators and demonstrate a link with the Poincare series of the uniformizing Fuchsian group. We show that Cϕ is compact if, and only if ϕ does not have a finite angular derivative at any point of the unit circle, thereby extending the result for univalent and finitely multivalent ϕ.

PublisherElsevier
JournalJournal of Functional Analysis
ISSN0022-1236
Publication dates
Print15 Feb 2015
Publication process dates
Deposited31 Oct 2014
Output statusPublished
Accepted author manuscript
Additional information

Available online 18 November 2014.

Digital Object Identifier (DOI)https://doi.org/10.1016/j.jfa.2014.11.003
LanguageEnglish
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