Angular derivatives and compactness of composition operators on Hardy spaces

Abstract

Let Do be a simply connected subdomain of the unit disk and A be a compact subset of Do. Let ϕ be a universal covering map for Do∖A. We prove that the composition operator Cϕ is compact on the Hardy space Hp if and only if ϕ does not have an angular derivative at any point of the unit circle. This result extends a theorem of M.M. Jones.