$L^p$ Quantitative Uncertainty Principles for the Generalized Fourier Transform Associated with the Spherical Mean Operator

Abstract

The aim of this paper is to prove new quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator. The first of these results is an extension of the Donoho and Stark's uncertainty principle. The second result extends the Heisenberg-Pauli-Weyl uncertainty principle. From these two results we deduce a continuous-time principle for the $L^p$ theory, when $1 \lt p \le 2$.