Local and nonlocal Poincaré inequalities on Lie groups

2021/07/19 by Tommaso Bruno, Bruno, Tommaso, Marco M. Peloso +3 · 1 citation
Mathematics · #26D10 #43A80 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2107.08664

openalex publication_date 2021/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a local L^p-Poincaré inequality, 1≤ p < ∞, on noncompact Lie groups endowed with a sub-Riemannian structure. We show that the constant involved grows at most exponentially with respect to the radius of the ball, and that if the group is nondoubling, then its growth is indeed, in general, exponential. We also prove a nonlocal L²-Poincaré inequality with respect to suitable finite measures on the group.

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• Poincaré inequalities on hyperbolic-type spaces

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