Quasi-invariance for heat kernel measures on sub-riemannian infinite-dimensional heisenberg groups

摘要

We study heat kernel measures on sub-Riemannian infinitedimensional Heisenberg-like Lie groups. In particular, we show that Cameron- Martin type quasi-invariance results hold in this subelliptic setting and give Lp-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.