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 $L^p$-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}. 
Fabrice Baudoin, Maria Gordina, and Tai Melcher
math.PR math.DG