# Journal of Operator Theory

Volume 82, Issue 1, Summer 2019 pp. 189-196.

Angular derivatives and compactness of composition operators on Hardy spaces

**Authors**:
Dimitrios Betsakos

**Author institution:**Department of Mathematics,
Aristotle University of Thessaloniki,
54124 Thessaloniki, Greece

**Summary: **Let $D_\mathrm o$ be a simply connected subdomain of the unit disk and $A$ be a compact subset of $D_\mathrm o$.
Let $\phi$ be a universal covering map for $D_\mathrm o\setminus A$. We prove that the composition operator
$C_\phi$ is compact on the Hardy space $H^p$ if and only if $\phi$ does not have an angular
derivative at any point of the unit circle. This result extends a theorem of M.M. Jones.

**DOI: **http://dx.doi.org/10.7900/jot.2018apr18.2196

**Keywords: **composition operator, Hardy space, universal covering map, angular derivative, Green function, Lindel\"of
principle

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