In this paper, we give an $L^p$ version of Hardy's uncertainty principles for a large class of integral and $q$-integral transforms. As an applications, we discuss an $L^p$ version of Hardy's theorem for the generalized Fourier transform associated with the Sturm-Liouville operator and for the Jacobi-Dunkl transform.
"An Essay Toward a Unified Theory of the $L^p$ Version of Hardy's Uncertainty Principles and $q$-Analogues." Commun. Math. Anal. 17 (1) 23 - 34, 2014.