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

TL;DR

This paper investigates the boundedness and convergence properties of the maximal operator associated with Bochner-Riesz means in Fourier-Bessel expansions, establishing weighted inequalities and almost everywhere convergence results.

Contribution

It provides new weighted and unweighted norm inequalities for the maximal operator and proves almost everywhere convergence for Fourier-Bessel Bochner-Riesz means.

Findings

Established boundedness of the maximal operator in weighted spaces.

Proved almost everywhere convergence of the Bochner-Riesz means.

Derived weak and restricted weak type inequalities at critical p.

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^{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.