Non local Poincaré inequalities on Lie groups with polynomial volume growth

2010/01/22 by Emmanuel Russ, Yannick Sire, Russ, Emmanuel +1
Mathematics · #Advanced Harmonic Analysis Research #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1001.4075

openalex publication_date 2010/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a real connected Lie group with polynomial volume growth, endowed with its Haar measure dx. Given a C² positive function M on G, we give a sufficient condition for an L² Poincaré inequality with respect to the measure M(x)dx to hold on G. We then establish a non-local Poincaré inequality on G with respect to M(x)dx.

Citations

• Balls and metrics defined by vector fields I: Basic properties

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