Weighted norm inequalities for the Opdam-Cherednik transform

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 Lp-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.