Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, Logroño 26004, Spain
Copyright © 2002 Óscar Ciaurri and Juan L. Varona. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be the modified Hankel transform
defined for suitable functions and extended to some spaces. Given , let
be the Bochner–Riesz operator for the Hankel transform. Also, we take the following generalization for the Hankel transform, and define as (thus, in particular,
). In the paper, we study the uniform boundedness of in
spaces when . We found that, for
(the critical index), the uniform boundedness of
is satisfied for every in the range . And, for the uniform boundedness happens if and only if
In the paper, the case (the corresponding generalization of the -multiplier for the Hankel transform) is previously analyzed; here, for . For this value of , the uniform
boundedness of is related to the convergence of Fourier–Neumann series.