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A Radial Integrability Result Concerning Bounded Functions in Analytic Besov Spaces with Applications

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Abstract

We prove that for every \(p\ge 1\) there exists a bounded function in the analytic Besov space \(B^p\) whose derivative is “badly integrable”  along every radius. We apply this result to study multipliers and weighted superposition operators acting on the spaces \(B^p\).

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Acknowledgements

We wish to thank the referee for reading carefully the paper and making a number of nice suggestions to improve it.

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  1. Análisis Matemático, Universidad de Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Salvador Domínguez & Daniel Girela

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  1. Salvador Domínguez
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  2. Daniel Girela
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Correspondence to Daniel Girela.

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This research is supported in part by a Grant from “El Ministerio de Economía y Competitividad”, Spain (PGC2018-096166-B-I00) and by Grants from la Junta de Andalucía (FQM-210 and UMA18-FEDERJA-002).

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Domínguez, S., Girela, D. A Radial Integrability Result Concerning Bounded Functions in Analytic Besov Spaces with Applications. Results Math 75, 67 (2020). https://doi.org/10.1007/s00025-020-01194-4

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