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arXiv · 2107.04090

Weighted Norm Inequalities for the Opdam--Cherednik Transform

Shyam Swarup Mondal·Anirudha Poria
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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.

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BibTeXRIS

Shyam Swarup Mondal, Anirudha Poria. 2021-07-08. Weighted Norm Inequalities for the Opdam--Cherednik Transform. https://doi.org/10.1142/s0129167x22500665

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