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 $L^p$-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.

Cited by in corpus (3)

• Hausdorff operators associated with the Opdam--Cherednik transform in Lebesgue spaces
• Uncertainty principles for the windowed Opdam--Cherednik transform
• The heat semigroup associated with the Jacobi--Cherednik operator and its applications