  We prove endpoint bounds for the square function associated with radial
Fourier multipliers acting on $L^{p}$ radial functions. This is a consequence
of endpoint bounds for a corresponding square function for Hankel multipliers.
We obtain a sharp Marcinkiewicz-type multiplier theorem for multivariate Hankel
multipliers and $L^p$ bounds of maximal operators generated by Hankel
multipliers as corollaries. The proof is built on techniques developed by
Garrig\'{o}s and Seeger for characterizations of Hankel multipliers.
