Sharp conditions for weighted integrability of $q$-Dunkl Fourier transforms

S. S. Volosivets

Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russia

Abstract: We obtain sufficient conditions for the weighted integrability of the $q$-Dunkl Fourier transforms of functions from generalized integral Lipschitz classes. In the $L^2$ case, we prove the sharpness of these conditions.

Keywords: $q$-Dunkl Fourier transform, $q$-Dunkl translation, modulus of smoothness, $q$-Dunkl differential operator.

UDC: 517.544

MSC: 44A15, 47A10

Received: 01.04.2025
Revised: 24.06.2025
Accepted: 27.06.2025

Language: English

DOI: 10.15393/j3.art.2025.17930