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

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 Ap theory and Hardy’s inequalities with weights. Moreover, we also obtain weighted weak type (1, 1) inequalities. The case when w(x) = xa is sketched and follows as a corollary of the main result. © 2006 Elsevier Inc. All rights reserved.