The aim of this paper is to establish a generalization of uncertainty principles for the q-Bessel Fourier transform, \(\mathcal {F}_{q, \nu }\) introduced earlier in Dhaouadi (Bull Math Anal Appl 5:42–60, 2013) and Dhaouadi (J Inequal Pure Appl Math 7:171, 2006). More precisely, we prove an \(\mathcal {L}_{q,p,\nu }\) -local uncertainty principle for \(\mathcal {F}_{q, \nu }\) , and we derive an \(\mathcal {L}_{q,p,\nu }\) version of the Heisenberg–Pauli–Weyl uncertainty principle. Furthermore, we establish three continuous uncertainty principles of concentration type. The first two principles are formulated in \(\mathcal {L}_{q,p,\nu }\) setting and depend on the concentration sets \(\Omega \) and \(\Sigma \) , as well as on the time function \(\varphi \) . The third uncertainty principle is also formulated in the \(\mathcal {L}_{q,p,\nu }\) setting, but it depends only on the sets of concentration and is independent of the bandlimited function \(\varphi \) . These \(\mathcal {L}_{q,p,\nu }\) -Donoho-Stark-type inequalities generalize the results obtained in the case \(p = q = 2\) .
