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

2012/07/24 by Ciaurri, Ó., Roncal, L.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1207.5749

Abstract

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^2ν+1dx). 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.

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