【数学与统计及交叉学科前沿论坛------高端学术讲座第144场】

报告题目：Geometric topics related to Besov type spaces on the Grushin setting

报告人：刘宇 北京科技大学教授

报告时间：2025年1月10日星期五11:00-12:00

报告地点：阜成路校区综合楼1116室

报告摘要：In this talk, we introduce some gtopics related to Besov type spaces on the Grushin setting. As we know, the Grushin spaces, as one of the most important models in the Carnot-Carath\'eodory space, are a class of locally compact and geodesic metric spaces which admit a dilation. Function spaces on Grushin spaces and some related geometric problems are always the research hotspots in this field.

Firstly, we investigate two classes of Besov type spaces based on and the fractional Grushin semigroup, respectively, and prove some important properties of these two Besov type spaces. Moreover, we also reveal the relationship between them.Secondly, we establish the isoperimetric inequality for thefractional perimeter, which is defined by the Grushin-Laplace operator on Grushin spaces. Finally, we combine the semigroup theory with a nonlocal calculus for the Grushin-Laplace operator to obtain the Sobolev type inequality. As an application, we also obtain the embedding theorem for Besov type spaces.

报告人简介：刘宇，北京科技大学数理学院教授，博士生导师，数理学院副院长，国家级一流本科专业建设点“数学与应用数学”负责人。一直从事调和分析及其应用、位势理论等方面的研究。主持完成国家自然科学基金面上项目2项，北京市自然科学基金面上项目1项、以及教育部等其他项目10余项，在包括J. Lond. Math. Soc.、Calc. Var. Partial Differential Equations、J. Geom. Anal. 等数学领域著名期刊上发表学术论文80余篇。2013年入选教育部新世纪优秀人才支持计划，2009年获得北京科技大学先进工作者。作为主要成员于2019年分别获得北京高校优秀本科育人团队和北京市工人先锋号；2020年获得北京市三八红旗集体；2021年获得全国工人先锋号等。