Logarithmic Derivatives of Heat Kernels and Logarithmic Sobolev Inequalities with Unbounded Diffusion Coefficients on Loop Spaces

Shigeki Aida

研究成果: Article査読

15 被引用数 (Scopus)

抄録

In this paper, we will give a sufficient condition on the logarithmic derivative of the heat kernel under which a logarithmic Sobolev inequality (LSI, in abbreviation) on a loop space holds. As an application, we prove an LSI on a pinned path space over the hyperbolic space Hn with constant sectional curvature -a (a≥0). The diffusion coefficient of the Dirichlet form is an unbounded but exponentially integrable function. Applying to the case when a=0, we can prove an LSI with a logarithmic Sobolev constant 18 in the case of standard pinned Brownian motion. Using the LSI on the pinned path space on Hn, we will prove an LSI on each homotopy class of the loop space over a constant negative curvature compact Riemannian manifold.

本文言語English
ページ(範囲)430-477
ページ数48
ジャーナルJournal of Functional Analysis
174
2
DOI
出版ステータスPublished - 2000 7 10

ASJC Scopus subject areas

  • Analysis

フィンガープリント 「Logarithmic Derivatives of Heat Kernels and Logarithmic Sobolev Inequalities with Unbounded Diffusion Coefficients on Loop Spaces」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル