WEIGHTED COMPOSITION OPERATORS BETWEEN WEIGHTED BLOCH TYPE SPACES

Abstract

Let $\mathrm{\mathbb{D}}$ be the open unit disk in the complex plane and $\mathrm{\phi }:\mathrm{\mathbb{D}}\to \mathrm{\mathbb{D}}$ as well as $\mathrm{\psi }:\mathrm{\mathbb{D}}\to \mathrm{\mathbb{C}}$ be analytic maps. For a holomorphic function f on $\mathrm{\mathbb{D}}$ the weighted composition operator C ϕ,ψ is defined by (C ϕ,ψ f)(z) = ψ(z)f(ϕ(z)) for every $\mathrm{z}\in \mathrm{\mathbb{D}}$ . We characterize when weighted composition operators acting between weighted Bloch type spaces are bounded resp. compact.