Coercive Inequalities on Metric Measure Spaces

By Waldemar Hebisch, B. Zegarlinski. 2009

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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.

Subfields: Applied Mathematics

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