Integrated Harnack inequalities on Lie groups
Differential Geometry
2008-08-01 v2 Probability
Abstract
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.
Cite
@article{arxiv.0711.4392,
title = {Integrated Harnack inequalities on Lie groups},
author = {Bruce K. Driver and Maria Gordina},
journal= {arXiv preprint arXiv:0711.4392},
year = {2008}
}
Comments
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