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

Understand

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}.