Malliavin calculus for Lie group-valued Wiener functions

Let G be a Lie group equipped with a set of left invariant vector fields. These vector fields generate a function \xi on Wiener space into G via the stochastic version of Cartan’s rolling map. It is shown here that, for any smooth function f with compact support, f(\xi) is Malliavin differentiable to all orders and these derivatives belong to L^p(\mu) for all p>1, where \mu is Wiener measure.