Norms of composition operators on weighted Hardy spaces

Abstract

The norm of a bounded composition operator induced by a disc automorphism is estimated on weighted Hardy spaces H 2(β) in which the classical Hardy space is continuously embedded. The estimate obtained is accurate in the sense that it provides the exact norm for particular instances of the sequence β. As a by-product of our results, an estimate for the norm of any bounded composition operator on H 2(β) is obtained.