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arXiv · 1108.1527

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

Fabrice Baudoin·Maria Gordina·Tai Melcher
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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 in \cite{BaudoinGarofalo2011}.

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Fabrice Baudoin, Maria Gordina, Tai Melcher. 2011-08-07. Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups. https://arxiv.org/abs/1108.1527

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