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Poincaré Inequality for Weighted First Order Sobolev Spaces on Loop Spaces

✍ Scribed by Fuzhou Gong; Michael Röckner; Wu Liming

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 268 KB
Volume: 185
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3775

No coin nor oath required. For personal study only.

✦ Synopsis

Taking lim sup L Ä lim k Ä in both sides of (2.10), by (i), (2.8), (2.9), and the fact that lim k Ä * k =1 we get a contradiction. Hence, , is not identically zero.

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In this paper we will prove the logarithmic Sobolev inequality on free loop groups for various heat kernel measures which P. Malliavin (1989Malliavin ( , 1991, in ``Diffusion Process and Related Problems in Analysis (M. A. Pinsley, Ed.), Vol. I, Birkha user, Basel) constructed. Those measures are as