Generalized Lipschitz classes in uniform metric and q-Dunkl Fourier transforms

For a function defined on \({\mathbb {R}}_q\) ${\mathbb{R}}_q$ we define two new variants of a modulus of smoothness and give a Boas type result about connection between the smoothness of this function and the behavior of its q-Dunkle Fourier transform near zero and at infinity.