Weighted norm inequalities for the Opdam–Cherednik transform

Abstract

In this paper, we study several weighted norm inequalities for the Opdam–Cherednik transform. We establish different versions of the Heisenberg–Pauli–Weyl inequality for this transform. In particular, we give an extension of this inequality using weights with different exponents and present a variation of the inequality that incorporates [Formula: see text]-norms for the Opdam–Cherednik transform. Also, we prove a version of the Hardy–Littlewood inequality for this transform. Finally, we give other variations of the Heisenberg–Pauli–Weyl inequality such as the Nash-type and Clarkson-type inequalities for the Opdam–Cherednik transform.