Weighted inequalities for the Bochner–Riesz means related to the Fourier–Bessel expansions

Abstract

We prove weighted inequalities for the Bochner–Riesz means for Fourier–Bessel series with more general weights w ( x ) than previously considered power weights. These estimates are given by using the local A p theory and Hardy's inequalities with weights. Moreover, we also obtain weighted weak type ( 1 , 1 ) inequalities. The case when w ( x ) = x a is sketched and follows as a corollary of the main result.