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

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 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.