Special operators on classical spaces of analytic functions

Abstract

In the first part of these notes we survey a number of results on composition operators on Hardy spaces and weighted Bergman spaces on the open unit disc D in C. In a straightforward manner we can identify such operators in the Bergman case as formal identities from the ambient spaces into Lebesgue spaces which are associated with so-called Carleson measures on D and we convince ourselves that the extension to Hardy spaces requires to take into account analogous measures on the closed disc D−−. We discuss measures of this kind along w Show more