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 var...

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Bibliographic Details
Published in:arXiv.org 2022-10
Main Authors: Mondal, Shyam Swarup, Poria, Anirudha
Format: Article
Language:English
Subjects:
Inequalities
Inequality
Norms
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2107.04090