## Illinois Journal of Mathematics

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

Matthew M. Jones

#### 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.

#### Article information

Source
Illinois J. Math., Volume 59, Number 3 (2015), 707-715.

Dates
Revised: 27 April 2016
First available in Project Euclid: 30 September 2016

https://projecteuclid.org/euclid.ijm/1475266405

Digital Object Identifier
doi:10.1215/ijm/1475266405

Mathematical Reviews number (MathSciNet)
MR3554230

Zentralblatt MATH identifier
1353.47052

#### Citation

Jones, Matthew M. Compact composition operators with symbol a universal covering map onto a multiply connected domain. Illinois J. Math. 59 (2015), no. 3, 707--715. doi:10.1215/ijm/1475266405. https://projecteuclid.org/euclid.ijm/1475266405

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