Martingale representation and log-Sobolev inequality on loop space

We obtain a martingale representation theorem for differentiable functions on loop space over a compact Riemannian manifold, which in turn yields a log-Sobolev inequality with a neat and explicit potential depending only on the curvature of the manifold and the Hessian of the heat kernel. Moreover, the potentiel term is L-p-integrable for all p greater than or equal to 1. (C) Academie des Sciences/Elsevier, Paris.MathematicsSCI(E)3ARTICLE6749-75332