Integrated Harnack inequalities on Lie groups
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 versio...
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| Veröffentlicht in: | Journal of differential geometry 2009-11, Vol.83 (3), p.501-550 |
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| container_title | Journal of differential geometry |
| container_volume | 83 |
| creator | Driver, Bruce K. Gordina, Maria |
| description | 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. |
| doi_str_mv | 10.4310/jdg/1264601034 |
| format | Article |
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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.</description><identifier>ISSN: 0022-040X</identifier><identifier>EISSN: 1945-743X</identifier><identifier>DOI: 10.4310/jdg/1264601034</identifier><language>eng</language><publisher>Lehigh University</publisher><ispartof>Journal of differential geometry, 2009-11, Vol.83 (3), p.501-550</ispartof><rights>Copyright 2009 Lehigh University</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c336t-f8b877857a96638b77ef945d12bc04dc3e9770fe1e15354f579fa9c6294cf55f3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,921,27903,27904</link.rule.ids></links><search><creatorcontrib>Driver, Bruce K.</creatorcontrib><creatorcontrib>Gordina, Maria</creatorcontrib><title>Integrated Harnack inequalities on Lie groups</title><title>Journal of differential geometry</title><description>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
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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.</abstract><pub>Lehigh University</pub><doi>10.4310/jdg/1264601034</doi><tpages>50</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of differential geometry, 2009-11, Vol.83 (3), p.501-550 |
| issn | 0022-040X 1945-743X |
| language | eng |
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| source | Project Euclid Complete |
| title | Integrated Harnack inequalities on Lie groups |
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