Uniform two-weight norm inequalities for Hankel transform Bochner-Riesz means of order one

Abstract

Two-weight $L^p$ norm inequalities, uniform with respect to the order of the involved Bessel function, are proved for the Bochner-Riesz means of the first order for the Hankel transform. Both sufficient and necessary conditions for parameters used in the two weights are determined. The proof relies on uniform pointwise asymptotic estimates for the Bessel functions that were shown by Barceló and Córdoba.