  The aim of the paper is to study the pinned Wiener measure on the loop space
over a simply connected compact Riemannian manifold together with the Hilbert
space structure induced by Mallianvin calculus and the induced Ornstein-
Uhlenbeck operator. We give a concrete estimate for the weak Poincare
inequality for the O-U Dirichlet form on loop space over simply connected
compact Riemannian manifold with strict positive Ricci curvature.
