Some examples of compact composition operators on H-2

摘要

We construct, in an essentially explicit way, various composition operators on H-2 and study their compactness or their membership in the Schatten classes. We construct: non-compact composition operators on H-2 whose symbols have the same modulus on the boundary of D as symbols whose composition operators are in various Schatten classes S-p with p > 2; compact composition operators which are in no Schatten class but whose symbols have the same modulus on the boundary of D as symbols whose associated composition operators are in S-p for every p > 2. (C) 2008 Elsevier Inc. All rights reserved.