Boas-Type Results for Fourier–Dunkl Expansion and Generalized Lipschitz Classes

We establish necessary and sufficient conditions for a function to belong to the generalized Lipschitz classes defined via the Dunkl translation, expressed in terms of the Fourier–Dunkl expansion. We also study the termwise differentiation of Fourier–Dunkl series. Our theorems generalize well-known results by Móricz for periodic functions involving classical Fourier series, and overlap with results previously obtained by Volosivets for Dunkl Fourier transforms. Some concluding remarks concerning our results are given at the end of the paper.