汇报标题 (Title)：Noncommutative logarithmic Sobolev inequalities
中文标题：非互换的对数Sobolev不等式
汇报人 (Speaker)：焦勇 教授（中南大学）
汇报功夫 (Time)：2024年4月10日(周三) 10:00
汇报地址 (Place)：腾讯会议（514-885-492）
约请人(Inviter)：席东盟、李晋、张德凯、吴加勇
主办部门：理学院数学系
汇报提要：We show that the logarithmic Sobolev inequality holds for an arbitrary hypercontractive semigroup acting on a noncommutative probability space. Particularly, we can recover the p-logarithmic Sobolev inequality whenever the Riesz transform is bounded. Our inequality applies to numerous concrete cases, including Poisson semigroups for free groups, the Ornstein-Uhlenbeck semigroup for mixed Q-gaussian von Neumann algebras, the free product for Ornstein-Uhlenbeck semigroups etc. This provides a unified abstract approach to logarithmic Sobolev inequalities in noncommutative setting.
