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Integration Operators in Average Radial Integrability Spaces of Analytic Functions

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Abstract

In this paper we characterize the boundedness, compactness, and weak compactness of the integration operators

$$\begin{aligned} T_g (f)(z)=\int _{0}^{z} f(w)g'(w)\ dw \end{aligned}$$

acting on the average radial integrability spaces RM(p, q). For these purposes, we develop different tools such as a description of the bidual of RM(p, 0) and estimates of the norm of these spaces using the derivative of the functions, a family of results that we call Littlewood–Paley type inequalities.

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Acknowledgements

We are grateful to Professor José Ángel Peláez for calling our attention to the paper [21] and to Professor Daniel Girela for some useful comments.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada II and IMUS, Escuela Técnica Superior de Ingeniería Universidad de Sevilla, Camino de los Descubrimientos, s/n, 41092, Sevilla, Spain

    Tanausú Aguilar-Hernández & Manuel D. Contreras

  2. Departmento de Análisis Matemático and IMUS, Facultad de Matemáticas Universidad de Sevilla, Calle Tarfia, s/n, 41012, Sevilla, Spain

    Luis Rodríguez-Piazza

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  1. Tanausú Aguilar-Hernández
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  2. Manuel D. Contreras
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  3. Luis Rodríguez-Piazza
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Correspondence to Manuel D. Contreras.

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This research was supported in part by Ministerio de Economía y Competitividad, Spain, and the European Union (FEDER), project PGC2018-094215-13-100, and Junta de Andalucía, FQM133 and FQM-104.

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Aguilar-Hernández, T., Contreras, M.D. & Rodríguez-Piazza, L. Integration Operators in Average Radial Integrability Spaces of Analytic Functions. Mediterr. J. Math. 18, 117 (2021). https://doi.org/10.1007/s00009-021-01774-w

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  • DOI: https://doi.org/10.1007/s00009-021-01774-w

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