Superposition operators between logarithmic Bloch spaces

  • Renny J. Malavé-Malavé
  • Julio C. Ramos-Fernández
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Abstract

We characterize all entire functions \(\phi \) that maps a logarithmic Bloch-type space \({\mathcal {B}}^\alpha _{\log ^\beta }\) into another of the same kind by superposition. As consequences of our study, we obtain several results about the boundedness of superposition operators acting between \(\alpha \)-Bloch spaces, Bloch–Orlicz spaces among others.

Keywords

Bloch-type spaces Superposition operator Entire function 

Mathematics Subject Classification

30D45 47B33 
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Notes

Acknowledgements

The authors wish to express their sincere gratitude to the anonymous referee for a thorough review and insightful suggestions.

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  • Renny J. Malavé-Malavé
    • 1
  • Julio C. Ramos-Fernández
    • 2
  1. 1.Departamento de MatemáticaUniversidad de OrienteCumanáVenezuela
  2. 2.Proyecto Curricular de Matemáticas, Facultad de Ciencias y EducaciónUniversidad Distrital Francisco José de CaldasBogotáColombia

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