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

The Bochner-Riesz means for Fourier-Bessel expansions: norm inequalities for the maximal operator and almost everywhere convergence