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系列学术活动之(107)

Iterated Weak and Weak Mixed Norms with Applications to Geometric Inequalities

发布者:澳门新葡8455最新网站   发布时间:2019-09-11  浏览次数:68



系列学术活动之(107)

题    目:

Iterated Weak and Weak Mixed Norms with Applications to Geometric Inequalities

摘    要:

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 can not control the other one.We give some convergence and completeness results for the two weak norms respectively. We study the convergence in truncated norm, which is a substitution of the convergence in measure for mixed Lebesgue spaces.  And we give a characterization of the convergence in truncated norm. We show that H\"older's inequality is not always true on mixed weak spaces  and we give a complete characterization of indices which admit   H\"older'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 人:

孙文昌,教授,南开大学

时    间:

201991415:00

地    点:

科技大楼617


报告人概况:

 孙文昌,南开大学数学科学学院教授。1970年生于山东省五莲县。1993年毕业于南开大学基础数学专业,1998年于南开大学数学学院获博士学位,2000年博士后出站并晋升副教授,2002年晋升教授,2003年评为博士生导师。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。

 孙文昌主要研究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, Journal of Functional Analysis, Mathematics of ComputationSCI期刊发表80多篇论文。

 孙文昌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),MicroSoft青年教授奖(2006年),教育部新世纪优秀人才支撑计划(2004年)。





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