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

2023/05/02 by Florian Fischer, Fischer, Florian, Norbert Peyerimhoff +1 · 1 citation
Mathematics · #26D10 #31C12 #58J60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2305.01288

openalex publication_date 2023/05/02 · openalex created_date 2023/05/04 · openalex updated_date 2026/07/28

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/Pinchover and Devyver/Pinchover and are motivated by corresponding results for hyperbolic spaces by Berchio/Ganguly/Grillo, and Berchio/Ganguly/Grillo/Pinchover.

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