On smoothness of extremizers to the Tomas-Stein inequality for one dimensional sphere

浙江大学数学科学学院九十周年院庆系列活动之十

题  目： On smoothness of extremizers to the Tomas-Stein inequality for one dimensional sphere

报告人:   邵双林（美国堪萨斯大学）

时  间:  2018年6月8日（周五）14：00--15：30，

地  点:  浙江大学玉泉校区欧阳楼316教室

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 arethe 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.

联系人：王成波老师（wangcbo@zju.edu.cn）

欢迎广大师生参加！