Weighted Norm Inequalities for the Opdam--Cherednik Transform
Functional Analysis
2022-10-17 v2
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 -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.
Cite
@article{arxiv.2107.04090,
title = {Weighted Norm Inequalities for the Opdam--Cherednik Transform},
author = {Shyam Swarup Mondal and Anirudha Poria},
journal= {arXiv preprint arXiv:2107.04090},
year = {2022}
}