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.

在本文中，我们证明了与傅立叶-贝塞尔展开相关的 Stein 平方函数的\(L^p\)估计。此外，我们证明了从傅立叶-贝塞尔级数到汉克尔变换的平方函数的转移结果。实际上，这些是贝塞尔设置中向量值乘法器从离散到连续的转移结果。因此，我们推断的范围的锐度p为\（L ^ P \）的从汉克尔斯坦平方函数对应的属性傅立叶-贝塞尔Stein的平方函数有界。最后，我们从 Stein 平方函数得到的估计值推导出傅立叶-贝塞尔乘法器的\(L^p\)估计值。