A Variation of uncertainty principles for the continuous wavelet transform connected with the Riemann–Liouville operator

Abstract

The aim of this paper is to prove a generalization of uncertainty principles for the continuous wavelet transform connected with the Riemann–Liouville operator in \(L^p\)-norm. More precisely, we establish the Heisenberg–Pauli–Weyl uncertainty principle, Donoho–Stark’s uncertainty principles and local Cowling-Price’s type inequalities. Finally, Pitt’s inequality and Beckner’s uncertainty principle are proved for this transform.