Discrete Fourier-Jacobi Transform and Generalized Lipschitz Classes

In this paper, we use the methods of Fourier-Jacobi harmonic analysis to generalize Boas-type results. We give necessary and sufficient conditions in terms of the Fourier-Jacobi coefficients of a function f in order to ensure that it belongs either to one of the generalized Lipschitz classes \({H}_{\alpha }^{m}\) and \({h}_{\alpha }^{m}\) for α > 0.