Hibschweiler Rita A., MacGregor Thomas H. Banach Spaces of Analytic Functions

American Mathematical Society, 2008. — 160 p.Banach spaces of analytic functions play an important role in both classical and modern analysis. In this Proceedings, the major focus is on spaces of functions analytic in the open unit disc, such as the Hardy spaces, the Bergman spaces, and the weighted versions of these spaces. Other spaces under consideration here include the Bloch space, the families of Cauchy transforms and fractional Cauchy transforms, BMO, VMO, and the Fock space. Some of the work deals with questions in several complex variables.One of the themes of the Proceedings is the notion of multiplication operators, composition operators and weighted composition operators acting on Banach spaces. This has been a topic of extensive research over the past twenty years. The Proceedings includes results characterizing bounded, compact and isometric composition operators in various settings.