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\(L^p\)-Boundedness of Stein’s Square Functions Associated with Fourier–Bessel Expansions

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Abstract

In this paper we prove \(L^p\) estimates for Stein’s square functions associated with Fourier–Bessel expansions. Furthermore, we prove transference results for square functions from Fourier–Bessel series to Hankel transforms. Actually, these are transference results for vector-valued multipliers from discrete to continuous in the Bessel setting. As a consequence, we deduce the sharpness of the range of p for the \(L^p\)-boundedness of Fourier–Bessel Stein’s square functions from the corresponding property for Hankel–Stein square functions. Finally, we deduce \(L^p\) estimates for Fourier–Bessel multipliers from that ones we have got for our Stein square functions.

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Acknowledgements

We would like to express our gratitude to the referee for his/her comments. The authors are partially supported by PID2019-106093GB-I00.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de La Laguna, Campus de Anchieta, Avda. Astrofísico Sánchez, s/n, 38721, La Laguna, Sta. Cruz de Tenerife, Spain

    Víctor Almeida, Jorge J. Betancor & Lourdes Rodríguez-Mesa

  2. Instituto de Matemática Aplicada del Litoral, UNL, CONICET, FIQ., Colectora Ruta Nac. N 168, Paraje El Pozo, S3007ABA, Santa Fe, Argentina

    Estefanía Dalmasso

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  1. Víctor Almeida
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  2. Jorge J. Betancor
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  3. Estefanía Dalmasso
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  4. Lourdes Rodríguez-Mesa
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Correspondence to Lourdes Rodríguez-Mesa.

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Almeida, V., Betancor, J.J., Dalmasso, E. et al. \(L^p\)-Boundedness of Stein’s Square Functions Associated with Fourier–Bessel Expansions. Mediterr. J. Math. 18, 177 (2021). https://doi.org/10.1007/s00009-021-01800-x

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  • DOI: https://doi.org/10.1007/s00009-021-01800-x

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