  In this paper, we develop a thorough analysis of the boundedness properties
of the maximal operator for the Bochner-Riesz means related to the
Fourier-Bessel expansions. For this operator, we study weighted and unweighted
inequalities in the spaces L^p((0,1),x^{2\nu+1}dx). Moreover, weak and
restricted weak type inequalities are obtained for the critical values of p. As
a consequence, we deduce the almost everywhere pointwise convergence of these
means.
