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arXiv · 1001.4075

Non local Poincaré inequalities on Lie groups with polynomial volume growth

Emmanuel Russ·Yannick Sire
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Abstract

Let $G$ be a real connected Lie group with polynomial volume growth, endowed with its Haar measure $dx$. Given a $C^2$ positive function $M$ on $G$, we give a sufficient condition for an $L^2$ 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 $M(x)dx$.

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Emmanuel Russ, Yannick Sire. 2010-01-22. Non local Poincaré inequalities on Lie groups with polynomial volume growth. https://arxiv.org/abs/1001.4075

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