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

ALMEIDA, VÍCTOR; BETANCOR, JORGE J.; DALMASSO, ESTEFANÍA; RODRÍGUEZ-MESA, LOURDES

MEDITERRANEAN JOURNAL OF MATHEMATICS

BIRKHAUSER VERLAG AG

Año: 2021 vol. 18

1660-5446

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.