报告主题：On smoothness of extremizers to the Tomas-Stein inequality for S^1
报告人：Shao Shuanglin 教授 （University of Kansas）
报告时间：2018年5月31日（周四）8:30
报告地点：校本部G507
邀请人：赵发友
主办部门：太阳成集团tyc33455数学系
报告摘要：In this talk, we discuss an aspect of the extremal problem for the Tomas-Stein inequality for the one dimensional sphere. The extremal problem usually includes whether these is an extremizer to the inequality; if they exist, what are the properties such as regularity or uniqueness? what are the exact form of extremizers? In this talk, we focus on establishing that extremizers to the Tomas-Stein inequality for one dimensional sphere are smooth. This is achieved by studying the associated generalized Euler-Lagrange inequality, which is a 5-fold convolution equation involving the surface measure of the sphere. The first step is to show that the extremizers gain an initial regularity depending on the functions themselves. Then we bootstrap this regularity to infinity. A key ingredient in this bootstrap argument is that the 5-fold convolution of the surface measures of sphere is uniformly bounded.
欢迎教师、员工参加 ！
