Composition followed by differentiation between weighted Bergman spaces and weighted Banach spaces of holomorphic functions

Abstract

Let Φ be an analytic self-map of the open unit disk D in the complex plane. Such a map induces through composition a linear composition operator CΦ : f ↦ f◦Φ.We are interested in the combination of CΦ with the differentiation operator D, that is in the operator DCΦ : f ↦ Φ` · (f ◦ Φ) acting between weighted Bergman spaces and weighted Banach spaces of holomorphic functions

Keywords

• composition operator
• differentiation operator
• weighted bergman spaces
• weighted banach spaces of holomorphic functions