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

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 Lp((0, 1), x2ν+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.