A variation on uncertainty principles for the generalized q-Bessel Fourier transform

The aim of this paper is to prove new uncertainty principles for the generalized q-Fourier Bessel transform studied earlier in [9]. To do so we prove a Nash-type inequality and a Carlson-type inequality for this transformation. From this we deduce a variation on Heisenberg's uncertainty inequality and Faris's local uncertainty principle. We also prove a variation on Donoho–Stark's uncertainty principle. Our results can be applied to the q-Bessel Fourier transform [7].