Geodesic
Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds
Emmanuel Russ1 ; Yannick Sire1
1Université Paul Cézanne LATP Faculté des Sciences et Techniques Case cour A Avenue Escadrille Normandie-Niemen F-13397 Marseille Cedex 20, France and CNRS, LATP, CMI 39 rue F. Joliot-Curie F-13453 Marseille Cedex 13, France
Studia Mathematica, Tome 203 (2011) no. 2, pp. 105-127
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $G$ be a real connected Lie group with polynomial volume growth endowed with its Haar measure $dx$. Given a $C^2$ positive bounded integrable 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 nonlocal Poincaré inequality on $G$ with respect to $M(x)\, dx$. We also give analogous Poincaré inequalities on Riemannian manifolds and deal with the case of Hardy inequalities.
DOI : 10.4064/sm203-2-1
Keywords: real connected lie group polynomial volume growth endowed its haar measure given positive bounded integrable function sufficient condition poincar inequality respect measure establish nonlocal poincar inequality respect analogous poincar inequalities riemannian manifolds hardy inequalities

Emmanuel Russ  1   ; Yannick Sire  1

1 Université Paul Cézanne LATP Faculté des Sciences et Techniques Case cour A Avenue Escadrille Normandie-Niemen F-13397 Marseille Cedex 20, France and CNRS, LATP, CMI 39 rue F. Joliot-Curie F-13453 Marseille Cedex 13, France 
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     title = {Nonlocal {Poincar\'e} inequalities on {Lie} groups with
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Emmanuel Russ; Yannick Sire. Nonlocal Poincaré inequalities on Lie groups with
 polynomial volume growth and Riemannian manifolds. Studia Mathematica, Tome 203 (2011) no. 2, pp. 105-127. doi: 10.4064/sm203-2-1

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