Integrated Harnack inequalities on Lie groups

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We show that the logarithmic derivatives of the convolution heat kernels on a uni-modular Lie group are exponentially integrable. This result is then used to prove an "integrated" Harnack inequality for these heat kernels. It is shown that this integrated Harnack inequality is equivalent to a version of Wang's Harnack inequality. (A key feature of all of these inequalities is that they are dimension independent.) Finally, we show these inequalities imply quasi-invariance properties of heat kernel measures for two classes of infinite dimensional "Lie" groups.
41 pages A section added where we show that this integrated Harnack inequality is equivalent to a version of Wang's Harnack inequality. New abstract

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Differential Geometry, Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/166106

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0711.4392
 http://arxiv.org/abs/0711.4392

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arXiv