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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups


Authors: Fabrice Baudoin, Maria Gordina and Tai Melcher
Journal: Trans. Amer. Math. Soc. 365 (2013), 4313-4350
MSC (2010): Primary 35K05, 43A15; Secondary 58J65
Published electronically: December 27, 2012
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Abstract | References | Similar Articles | Additional Information

Abstract: We study heat kernel measures on sub-Riemannian infinite-
dimensional Heisenberg-like Lie groups. In particular, we show that Cameron-Martin type quasi-invariance results hold in this subelliptic setting and give $ L^p$-estimates for the Radon-Nikodym derivatives. The main ingredient in our proof is a generalized curvature-dimension estimate which holds on approximating finite-dimensional projection groups. Such estimates were first introduced by Baudoin and Garofalo.


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Additional Information

Fabrice Baudoin
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: fbaudoin@math.purdue.edu

Maria Gordina
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: maria.gordina@uconn.edu

Tai Melcher
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
Email: melcher@virginia.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05778-3
PII: S 0002-9947(2012)05778-3
Received by editor(s): August 12, 2011
Received by editor(s) in revised form: December 13, 2011
Published electronically: December 27, 2012
Additional Notes: The first author’s research was supported in part by NSF Grant DMS-0907326.
The second author’s research was supported in part by NSF Grant DMS-1007496.
The third author’s research was supported in part by NSF Grant DMS-0907293
Dedicated: To Len Gross
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.