INVARIANT SOBOLEV CALCULUS ON THE FREE LOOP SPACE

We give integration by parts formulas over the free loop space of a co mpact riemannian manifold, after discussing the tangent space. We give a Sobolev Calculus based upon the H-derivative, after introducing som e connections. We define an invariant by relation Ornstein-Uhlenbeck o perator over it. Some examples of smooth functionals are studied.