Non local Poincaré inequalities on Lie groups with polynomial volume growth

Details Non local Poincaré inequalities on Lie groups with polynomial volume growth Non local Poincaré inequalities on Lie groups with polynomial volume growth

2010-01-22

arxiv.org/abs/1001.4075v1

Mathematics

Functional Analysis

Scientific paper

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 $L^2$ Poincar\'e inequality with respect to the
measure $M(x)dx$ to hold on $G$. We then establish a non-local Poincar\'e
inequality on $G$ with respect to $M(x)dx$.

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