Logarithmic Sobolev Inequality on Free Loop Groups for Heat Kernel Measures Associated with the General Sobolev Spaces

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

In this paper we will prove the logarithmic Sobolev inequality on free loop groups for various heat kernel measures which P. Malliavin (1989, 1991, in "Diffusion Process and Related Problems in Analysis (M. A. Pinsley, Ed.), Vol. I, Birkhäuser, Basel) constructed. Those measures are associated with the Sobolev spaces of order s (s>1/2) of the free loops in the Lie algebra. We will equipp the free loop groups with those metrics and will show that a formula of Weitzenböck type holds, which enables us to apply the method of Driver and Lohrenz (1996, J. Funct. Anal.146, 381-448).

Original languageEnglish
Pages (from-to)170-213
Number of pages44
JournalJournal of Functional Analysis
Volume179
Issue number1
DOIs
Publication statusPublished - Jan 10 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis

Fingerprint Dive into the research topics of 'Logarithmic Sobolev Inequality on Free Loop Groups for Heat Kernel Measures Associated with the General Sobolev Spaces'. Together they form a unique fingerprint.

Cite this