报告题目 (Title)：球Banach函数空间中的BBM、BVY和BSVY公式
报告人 (Speaker)：杨大春 教授（北京师范大学）
报告时间 (Time)：2025年9月4日（周四） 15:30
报告地点 (Place)：校本部 GJ303
邀请人(Inviter)：赵发友 教授
主办部门：理学院数学系
报告摘要：The concept of ball quasi-Banach function (BQBF) spaces was introduced in 2017 by Y. Sawano, K.-P. Ho, D. Yang, and S. Yang. It is well known that some well-known function spaces, such as Morrey spaces, weighted Lebesgue spaces, mixed-norm Lebesgue spaces, and Orlicz-slice spaces, are ball quasi-Banach function spaces, but not quasi-Banach func- tion spaces. In this talk, we will first recall the celebrated (BBM) formulae of J. Bourgain, H. Brezis, and P. Mironescu and the recent surprising (BVY and BSVY) formulae of H. Brezis, A. Seeger, J. Van Schaftingen, and P.-L. Yung. Then we will introduce some recent extensions of these formulae to Sobolev spaces associated with ball Banach function spaces. In particular, we will introduce some methods on how to overcome the difficulties caused by the lack of the translation invariance, the rotation invariance, and the explicit expression of the quasi-norm of BQBF spaces under consideration.
