On the generalized Dunkl Dini–Lipschitz spaces

Abstract

In this paper we introduce function spaces denoted by () as subspaces of associated with -generalized Fourier transform arising from the Dunkl theory, that we call generalized Dunkl Dini–Lipschitz spaces. Firstly, for , we provide characterizations of these spaces by means modulus of continuity. Moreover, we obtain behaviour estimations related to -generalized Fourier transform for and , and for we obtain an analogue of Titchmarsh's theorem in . In the sequel, we introduce the modulus of smoothness related to the -generalized Fourier transform for which we derive some of its properties on the Sobolev type space denoted by .