Non local Poincaré inequalities on Lie groups with polynomial volume growth

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 $M(x)dx$.

References in corpus (1)

• Fractional Poincaré inequalities for general measures