$L^p$ LOCAL UNCERTAINTY PRINCIPLE FOR THE DUNKL TRANSFORM

Abstract

In this paper, we establish $L^p$ local uncertainty principle for the Dunkl transform on Rd; and we deduce $L^p$ version of the Heisenberg-Pauli- Weyl uncertainty principle for this transform. We use also the $L^p$ local uncertainty principle for the Dunkl transform and the techniques of Donoho-Stark, we obtain uncertainty principles of concentration type in the $L^p$ theory, when 1 < p < 2.