Coercive Inequalities on Metric Measure Spaces
Functional Analysis
2009-05-13 v1 Probability
Abstract
We study coercive inequalities on finite dimensional metric spaces with probability measures which do not have volume doubling property. This class of inequalities includes Poincar\'e and Log-Sobolev inequality. Our main result is proof of Log-Sobolev inequality on Heisenberg group equipped with either heat kernel measure or "gaussian" density build from optimal control distance. As intermediate results we prove so called U-bounds.
Cite
@article{arxiv.0905.1713,
title = {Coercive Inequalities on Metric Measure Spaces},
author = {W. Hebisch and B. Zegarlinski},
journal= {arXiv preprint arXiv:0905.1713},
year = {2009}
}