Sharp Hardy-type inequalities for non-compact harmonic manifolds and Damek–Ricci spaces

Fischer, Florian; Peyerimhoff, Norbert

Abstract

We show various sharp Hardy-type inequalities for the linear and quasi-linear Laplacian on non-compact harmonic manifolds with a particular focus on the case of Damek–Ricci spaces. Our methods make use of the optimality theory developed by Devyver, Fraas and Pinchover and Devyver and Pinchover and are motivated by corresponding results for hyperbolic spaces by Berchio, Ganguly and Grillo, and Berchio, Ganguly, Grillo and Pinchover.

Citation

Fischer, F., & Peyerimhoff, N. (online). Sharp Hardy-type inequalities for non-compact harmonic manifolds and Damek–Ricci spaces. Israel Journal of Mathematics, https://doi.org/10.1007/s11856-024-2713-y

• Journal Article Type: Article
• Acceptance Date: Dec 21, 2023
• Online Publication Date: Jan 20, 2025
• Deposit Date: Mar 27, 2025
• Publicly Available Date: Mar 27, 2025
• Journal: Israel Journal of Mathematics
• Print ISSN: 0021-2172
• Electronic ISSN: 1565-8511
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1007/s11856-024-2713-y
• Public URL: https://durham-repository.worktribe.com/output/3743580