Abstract
Let \({\phi}\) be an analytic self-map of the open unit disk \({\mathbb{D}}\) in the complex plane. This map induces a composition operator followed by differentiation \({DC_{\phi}}\) acting between weighted Banach spaces of holomorphic functions. We give a characterization for such an operator to be bounded resp. compact in terms of the involved weights as well as the function \({\phi}\) .
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Wolf, E. Composition followed by differentiation between weighted Banach spaces of holomorphic functions. RACSAM 105, 315–322 (2011). https://doi.org/10.1007/s13398-011-0040-8
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DOI: https://doi.org/10.1007/s13398-011-0040-8