English

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.

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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