A variation of the Lq,p‐uncertainty inequalities of Heisenberg‐type for symmetric q‐integral transforms

Abstract

The aim of this paper is to prove new uncertainty inequalities of Heisenberg‐type for a q‐integral operator with a bounded kernel. To do so, we prove a Nash and Carlson's inequalities for this transformation on for 1 < p≤2, on for 1 < p < 2, and on for 1 < p1 < p2≤2. Our results can be applied to the the q‐Fourier‐cosine transform, the q‐Dunkl transform, and the q‐Bessel‐Fourier transform.