Fourier–Bessel transforms from generalized Lipschitz spaces and weighted Lebesgue spaces

Abstract

We prove a dual Boas type result connecting the behavior of a function and the smoothness of its Fourier–Bessel transform. We obtain sufficient conditions for the weighted integrability of Fourier–Bessel transforms in terms of the moduli of smoothness connected with Bessel translation operators. In some particular case we prove the sharpness of this result. Also we prove a Boas type result about integrability of generalized contractions.