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

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 Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-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.