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

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