Integrated Harnack inequalities on Lie groups
Integrated Harnack inequalities on Lie groups
复制标题
李群上的积分 Harnack 不等式
DOI：
10.4310/jdg/1264601034
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发表时间：
2007
影响因子：
2.5
通讯作者：
M. Gordina
中科院分区：
文献类型：
--
作者：
B. Driver;M. Gordina
我们证明单模李群上卷积热核的对数导数是指数可积的。然后，该结果用于证明这些热核的“积分”Harnack 不等式。结果表明，这种积分 Harnack 不等式相当于 Wang 的 Harnack 不等式的一个版本。 （所有这些不等式的一个关键特征是它们与维度无关。）最后，我们证明这些不等式意味着两类无限维“李”群的热核测度的准不变性。
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.