Abstract
The aim of this paper is to prove new uncertainty inequalities of Heisenberg-type for a q-integral operator Tq with a bounded kernel. To do so, we prove a Nash and Carlson's inequalities for this transformation on Lq,1 boolean AND Lq,p(omega,|omega(x)|dqx) for 1 < p <= 2, on Lq,2 boolean AND Lq,p(omega,|omega(x)|dqx) for 1 < p < 2, and on Lq,p1 boolean AND Lq,p2(omega,|omega(x)|dqx) for 1 < p(1) < p(2)<= 2. Our results can be applied to the the q-Fourier-cosine transform, the q-Dunkl transform, and the q-Bessel-Fourier transform.