Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds

Emmanuel Russ, and Yannick Sire. "Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds." Studia Mathematica 203.2 (2011): 105-127. <http://eudml.org/doc/285453>.

@article{EmmanuelRuss2011,
abstract = {Let G be a real connected Lie group with polynomial volume growth endowed with its Haar measuredx. Given a C² positive bounded integrable function M on G, we give a sufficient condition for an L² 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.},
author = {Emmanuel Russ, Yannick Sire},
journal = {Studia Mathematica},
keywords = {Lie groups; Riemannian manifolds; polynomial volume growth; nonlocal inequalities; fractional powers of operators},
language = {eng},
number = {2},
pages = {105-127},
title = {Nonlocal Poincaré inequalities on Lie groups with polynomial volume growth and Riemannian manifolds},
url = {http://eudml.org/doc/285453},
volume = {203},
year = {2011},
}

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
VL - 203
IS - 2
SP - 105
EP - 127
AB - Let G be a real connected Lie group with polynomial volume growth endowed with its Haar measuredx. Given a C² positive bounded integrable function M on G, we give a sufficient condition for an L² 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.
LA - eng
KW - Lie groups; Riemannian manifolds; polynomial volume growth; nonlocal inequalities; fractional powers of operators
UR - http://eudml.org/doc/285453
ER -