The log-Sobolev inequality on loop space over a compact Riemannian manifold
type: Item
instance of: scholarly article
title: The log-Sobolev inequality on loop space over a compact Riemannian manifold
zbMATH Open document ID: 0909.22036
author: Fu-Zhong Gong
author: Zhi-Ming Ma
published in: Journal of Functional Analysis
publication date: 1998-10-14T00:00:00Z
review text: The authors obtain a log-Sobolev inequality with a neat and explicit potential for the gradient on a based loop space over a compact Riemannian manifold. The potential term depends only on the Ricci curvature of the manifold and the Hessian of the heat kernel, and is \(L^p\)-integrable for all \(p\geq 1\). The log-Sobolev inequality is obtained as a consequence of a martingale representation theorem for the differentiable functions on the loop space which is a variation of the Clark-Ocone-Haussman formula.
Mathematics Subject Classification ID: 22E67
Mathematics Subject Classification ID: 58J65
zbMATH DE Number: 1211646
zbMATH Keywords: log-Sobolev inequality
zbMATH Keywords: loop space
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: heat kernel
zbMATH Keywords: martingale representation theorem
zbMATH Keywords: Clark-Ocone-Haussman formula
reviewed by: Constantin Udrişte
MaRDI profile type: Publication
full work available at URL: jfan.1998.3263
OpenAlex ID: W1996923978
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DOI: 10.1006/JFAN.1998.3263
description: scientific article; zbMATH DE number 1211646