Integrated Harnack inequalities on Lie groups

Details Integrated Harnack inequalities on Lie groups Integrated Harnack inequalities on Lie groups

2007-11-28

arxiv.org/abs/0711.4392v2

Mathematics

Differential Geometry

41 pages A section added where we show that this integrated Harnack inequality is equivalent to a version of Wang's Harnack in

Scientific paper

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.

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