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+1dx). Moreover, weak and restricted weak type inequalities are obtained for the critical values of pp. As a consequence, we deduce the almost everywhere pointwise convergence of these means.