On estimates for the q-analogue of Dunkl transform in the weighted space \(L^{2}_{q,\alpha }(\mathbb {R}_{q})\)

Abstract

In this paper, using some elements of the q-harmonic analysis associated to the q-Dunkl operator introduced in [3], for fixed \(0<q<1\), some new estimates useful in applications are proved for the generalized q-Dunkl transform in the space \(L^{2}_{q,\alpha }(\mathbb {R}_{q})\) as applied to some classes of functions characterized by a generalized modulus of continuity.