Coercive Inequalities on Metric Measure Spaces

Details Coercive Inequalities on Metric Measure Spaces Coercive Inequalities on Metric Measure Spaces

2009-05-11

arxiv.org/abs/0905.1713v1

Mathematics

Functional Analysis

Scientific paper

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.

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