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arXiv · 1912.08527

$L^p$--boundedness of Stein's square functions associated to Fourier--Bessel expansions

Víctor Almeida·Jorge J. Betancor·Estefanía Dalmasso·Lourdes Rodríguez-Mesa
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Abstract

In this paper we prove $L^p$ estimates for Stein's square functions associated to 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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Víctor Almeida, Jorge J. Betancor, Estefanía Dalmasso, Lourdes Rodríguez-Mesa. 2019-12-18. $L^p$--boundedness of Stein's square functions associated to Fourier--Bessel expansions. https://arxiv.org/abs/1912.08527

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