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

Elke Wolf

doi:10.2478/ausm-2014-0021

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 C_Φ : f ↦ f◦Φ.We are interested in the combination of C_Φ with the differentiation operator D, that is in the operator DC_Φ : f ↦ Φ` · (f ◦ Φ) acting between weighted Bergman spaces and weighted Banach spaces of holomorphic functions

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

Abstract

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