Nonlocal Poincaré inequalities on Lie groups with
polynomial volume growth and Riemannian manifolds
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
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.
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
Affiliations des auteurs :
Emmanuel Russ 1 ; Yannick Sire 1
@article{10_4064_sm203_2_1,
author = {Emmanuel Russ and Yannick Sire},
title = {Nonlocal {Poincar\'e} inequalities on {Lie} groups with
polynomial volume growth and {Riemannian} manifolds},
journal = {Studia Mathematica},
pages = {105--127},
year = {2011},
volume = {203},
number = {2},
doi = {10.4064/sm203-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm203-2-1/}
}
TY - JOUR AU - Emmanuel Russ AU - Yannick Sire TI - Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds JO - Studia Mathematica PY - 2011 SP - 105 EP - 127 VL - 203 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm203-2-1/ DO - 10.4064/sm203-2-1 LA - en ID - 10_4064_sm203_2_1 ER -
%0 Journal Article %A Emmanuel Russ %A Yannick Sire %T Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds %J Studia Mathematica %D 2011 %P 105-127 %V 203 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/sm203-2-1/ %R 10.4064/sm203-2-1 %G en %F 10_4064_sm203_2_1
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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