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Superposition operators between logarithmic Bloch spaces

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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.

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Acknowledgements

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

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Authors and Affiliations

  1. Departamento de Matemática, Universidad de Oriente, Cumaná, 6101, Edo. Sucre, Venezuela

    Renny J. Malavé-Malavé

  2. Proyecto Curricular de Matemáticas, Facultad de Ciencias y Educación, Universidad Distrital Francisco José de Caldas, Carrera 3 No. 26 A-40, Bogotá, Colombia

    Julio C. Ramos-Fernández

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  1. Renny J. Malavé-Malavé
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  2. Julio C. Ramos-Fernández
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Correspondence to Julio C. Ramos-Fernández.

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Malavé-Malavé, R.J., Ramos-Fernández, J.C. Superposition operators between logarithmic Bloch spaces. Rend. Circ. Mat. Palermo, II. Ser 68, 105–121 (2019). https://doi.org/10.1007/s12215-018-0345-y

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  • DOI: https://doi.org/10.1007/s12215-018-0345-y

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