Composition operators on analytic Lipschitz spaces

Abstract

If X X is a Banach space of functions analytic on the disk and φ : D → D \varphi :{\mathbf {D}} \to {\mathbf {D}} is analytic, one can define the composition operator C φ {C_\varphi } on X X by C φ f := f ∘ φ {C_\varphi }f: = f \circ \varphi . This paper discusses the boundedness and w w -compactness of composition operators on the analytic Lipschitz spaces A α , 0 > α > 1 {\mathcal {A}_\alpha },\;0 > \alpha > 1 .