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An Essay Toward a Unified Theory of the $L^p$ Version of Hardy's Uncertainty Principles and $q$-Analogues

Commun. Math. Anal.
Volume 17, Number 1 (2014), 23 - 34

An Essay Toward a Unified Theory of the $L^p$ Version of Hardy's Uncertainty Principles and $q$-Analogues

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Abstract

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.