Hardy-Rellich and second order Poincar\'e identities on the hyperbolic space via Bessel pairs
Analysis of PDEs
2022-05-06 v1
Abstract
We prove a family of Hardy-Rellich and Poincar\'e identities and inequalities on the hyperbolic space having, as particular cases, improved Hardy-Rellich, Rellich and second order Poincar\'e inequalities. All remainder terms provided considerably improve those already known in literature, and all identities hold with same constants for radial operators also. Furthermore, as applications of the main results, second order versions of the uncertainty principle on the hyperbolic space are derived.
Keywords
Cite
@article{arxiv.2106.03166,
title = {Hardy-Rellich and second order Poincar\'e identities on the hyperbolic space via Bessel pairs},
author = {Elvise Berchio and Debdip Ganguly and Prasun Roychowdhury},
journal= {arXiv preprint arXiv:2106.03166},
year = {2022}
}
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22 Pages