Logarithmic Sobolev Inequality on Free Loop Groups for Heat Kernel Measures Associated with the General Sobolev Spaces
Logarithmic Sobolev Inequality on Free Loop Groups for Heat Kernel Measures Associated with the General Sobolev Spaces
复制标题
与一般Sobolev空间相关的热核测度的自由循环群上的对数Sobolev不等式
DOI：
10.1006/jfan.2000.3677
复制
发表时间：
2001
影响因子：
1.7
通讯作者：
Y. Inahama
中科院分区：
文献类型：
--
作者：
Y. Inahama
本文证明了P. Malliavin（1989，1991）在“Diffusion Process and Related Problems in Analysis（M. A. Pinsley，编），Vol. I，Birkhauser，巴塞尔）构建。这些测度与李代数中自由环的s（s >1/2）阶Sobolev空间相联系。我们将装备的自由循环组与这些指标，并将表明，公式的Weitzenbock类型的持有，这使我们能够应用的方法驱动程序和Lozenz（1996年，J.功能。Anal. 146，381-448）。
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, Birkhauser, 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 Weitzenbock type holds, which enables us to apply the method of Driver and Lohrenz (1996, J. Funct. Anal. 146 , 381–448).