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