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 language | English |
|---|---|
| Pages (from-to) | 170-213 |
| Number of pages | 44 |
| Journal | Journal of Functional Analysis |
| Volume | 179 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 10 2001 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Analysis
Cite this
Logarithmic Sobolev Inequality on Free Loop Groups for Heat Kernel Measures Associated with the General Sobolev Spaces. / Inahama, Yuzuru.
In: Journal of Functional Analysis, Vol. 179, No. 1, 10.01.2001, p. 170-213.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Logarithmic Sobolev Inequality on Free Loop Groups for Heat Kernel Measures Associated with the General Sobolev Spaces
AU - Inahama, Yuzuru
PY - 2001/1/10
Y1 - 2001/1/10
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=0012995671&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0012995671&partnerID=8YFLogxK
U2 - 10.1006/jfan.2000.3677
DO - 10.1006/jfan.2000.3677
M3 - Article
AN - SCOPUS:0012995671
VL - 179
SP - 170
EP - 213
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
ER -