A Concrete Estimate For The Weak Poincare Inequality On Loop Space

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.