Coercive Inequalities on Metric Measure Spaces
Coercive Inequalities on Metric Measure Spaces
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DOI：
10.1016/j.jfa.2009.05.016
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发表时间：
2009-05
期刊：
影响因子：
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通讯作者：
W. Hebisch;B. Zegarlinski
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文献类型：
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作者：
W. Hebisch;B. Zegarlinski
我们研究了有限维度量空间上不具有体积倍增性质的概率度量的强制不等式。这类不等式包括Poincar-‘e和Log-Sobolev不等式.我们的主要结果是证明了Heisenberg群上的Log-Sobolev不等式，它配备了热核度量或从最优控制距离构造的“Gauss型”密度.作为中间结果，我们证明了所谓的U-界.
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.