Abstract
The aim of this paper is to prove new uncertainty principles for integral operators tau with bounded kernel for which there is a Plancherel Theorem. The first of these results is an extension of Faris's local uncertainty principle which states that if a nonzero function f is an element of L-2 (R-d, mu) is highly localized near a single point then tau(f) cannot be concentrated in a set of finite measure. The second result extends the Benedicks-Amrein-Berthier uncertainty principle and states that a nonzero function f is an element of L-2 (R-d, mu) and its integral transform tau(f) cannot both have support of finite measure. From these two results we deduce a global uncertainty principle of Heisenberg type for the transformation tau. We apply our results to obtain new uncertainty principles for the Dunkl and Clifford Fourier transforms.