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Monatshefte für Mathematik

, Volume 190, Issue 4, pp 725–734 | Cite as

Sequences of zeros of analytic function spaces and weighted superposition operators

  • Salvador Domínguez
  • Daniel GirelaEmail author
Article
  • 85 Downloads

Abstract

We use properties of the sequences of zeros of certain spaces of analytic functions in the unit disc \({\mathbb {D}}\) to study the question of characterizing the weighted superposition operators which map one of these spaces into another. We also prove that for a large class of Banach spaces of analytic functions in \({\mathbb {D}}\), Y, we have that if the superposition operator \(S_\varphi \) associated to the entire function \(\varphi \) is a bounded operator from X, a certain Banach space of analytic functions in \(\mathbb D\), into Y, then the superposition operator \(S_{\varphi ^\prime }\) maps X into Y.

Keywords

Weighted superposition operator Sequence of zeros Bloch function Bergman spaces Weighted Banach spaces of analytic functions 

Mathematics Subject Classification

Primary 30H30 30H20 Secondary 46E15 47H99 

Notes

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Análisis Matemático, Facultad de CienciasUniversidad de MálagaMálagaSpain

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