勷勤数学•专家报告

题      目：A Bourgain-Gromov problem on non-compact Sobolev and Besov embeddings

报  告  人： 姚力丁 助理教授  (邀请人：范智杰)

                                    Purdue University Fort Wayne

时      间： 6月7日  16：00-17:00

地     点：数科院东楼401

报告人简介:

       姚力丁，普渡大学韦恩堡分校助理教授。2022年于美国威斯康星大学麦迪逊分校取得博士学位，后于俄亥俄州立大学任博士后。姚力丁主要从事调和分析方面的研究，以及调和分析在微分几何、多复变函数以及函数空间方向上的应用。目前在Amer. Jour. of Math, Trans. of AMS, J. Funct. Anal, J. Anal. Math.等国际数学期刊上共发表论文13篇

摘      要：

       In this talk we will introduce certain weak compactness conditions for bounded linear maps, called strictly and finitely strictly singular. We give a classification of all non-compact embedding between Besov spaces, both on bounded domains and on $\Bbb R^n$, that are finitely strictly singular or strictly singular. As a direct application, we give a simple proof that the Sobolev-Lorentz embedding $W_0^{1,p}(\Omega)\to L^{p^*,q}(\Omega)$ for $\Omega\subset\Bbb R^n$, $p^*=\frac{np}{n-p}$, $p<q\le\infty$ is finitely strictly singular, which simplifies the previous work by Lang-Mihula. This is a joint work with Chian Yeong Chuah and Jan Lang.

          欢迎老师、同学们参加、交流！