报告题目1：Weak Mixed-Norms and Iterated Weak Norms in Lebesgue Spaces

报告时间：09:00

报告人简介：

孙文昌，南开大学数学科学学院教授、博士生导师。曾访问中国科学院晨兴数学中心、维也纳大学数学系、丹麦科技大学数学系和薛定谔国际数学物理研究所等。主要研究领域：小波分析与调和分析，多次主持国家自然科学基金和教育部博士学科点基金项目，在Advances in Mathematics, Mathematische Annalen, Journal of Functional Analysis, Applied and Computational Harmonic Analysis, Mathematics of Computation等SCI期刊发表80多篇论文。

孙文昌教授曾获得国家杰出青年科学基金（2015），国务院政府特殊津贴（2010年度），天津市自然科学一等奖（第一完成人，2008年），天津青年科技奖（2008年），微软青年教授奖（2006年），教育部新世纪优秀人才支持计划（2004年）。

报告简介：

We consider weak norms in Lebesgue spaces with mixed norms. We study properties of the weak mixed-norm and the iterated weak norm and present the relationship between the two weak norms.

Even for the ordinary Lebesgue spaces, the two weak norms are not equivalent and any one of them cannot control the other one. We show that Hölder's inequality is not always true on mixed weak spaces and we give a complete characterization of indices which admit Hölder's inequality.

As applications, we establish some geometric inequalities related to fractional integrals in mixed weak spaces and in iterated weak spaces respectively, which essentially generalize the Hardy-Littlewood-Sobolev inequality.

报告题目2：Effect of perturbation on the attainability of sharp Trudinger-Moser inequality and Concentration-Compactness limit

报告时间：10:30

报告人简介：

陈露，北京理工大学英国威廉希尔公司官网副研究员。主要研究领域为几何分析与偏微分方程，目前主要研究兴趣为稳定的极小曲面和Allen-Cahn方程。相关工作发表在Adv. Math, Trans. AMS, J. Funct. Anal, Calc. Var & PDE等国际知名SCI学术期刊，主持国家自然科学基金青年基金一项。

报告简介：

In this talk, I will first give a survey about the history of sharp Trudinger-Moser inequality and introduce our recent work on extremals of critical Adams inequality in unbounded domain. Then, I will introduce a maximization problem on the Trudinger-Moser inequality and clarify the effect of lower order perturbation on the attainability of the best constant. As an application, I also study the accurate supremum of concentration compactness sequence and obtained the Carleson-Chang limit for Adams inequalities which remain open for many years. Our method is based on delicate estimate of energy for maximizer and capacity analysis.