报告题目：Brezis-Van Schaftingen-Yung and Bourgain-Brezis-Mironescu Formulae in Ball Banach Function Spaces

主讲人：袁文教授

单位：北京师范大学

时间：5月18日10:00

腾讯ID：359-664-218

密码：051866

摘要：Let $X$ be a Ball Banach function space. In this talk, we first recall the Bourgain-Brezis-Mironescu and the Brezis-Van Schaftingen-Yung formulae related to of the Sobolev space $W^{1,1}(\mathbb{R}^n)$. Then, under some mild assumptions, and via a new method involving extrapolation, we establish the Brezis-Van Schaftingen-Yung formula and the Bourgain-Brezis-Mironescu formula in a more general setting of Ball Banach function space $X$. This generalization has a wide range of applications and, particularly, enables us to establish new fractional Sobolev and Gagliardo-Nirenberg inequalities in various function spaces, including Morrey spaces, mixed-norm Lebesgue spaces, variable Lebesgue spaces, weighted Lebesgue spaces, Orlicz spaces, and Orlicz-slice (generalized amalgam) spaces.

简 介：袁文，北京师范大学数学科学学院教授，主要从事调和分析特别是函数空间实变理论与算子有界性方面的研究，已在欧氏空间与齐型空间上的Hardy空间、Morrey空间、Besov空间及Triebel-Lizorkin空间等各种函数空间的实变理论及其应用方面取得了一系列学术成果，部分成果发表于Adv. Math.、ACHA、JFA、JMPA、CVPDE和Trans. AMS等知名数学期刊上；曾获优秀青年科学基金、教育部自然科学奖二等奖（排名第二）、德国洪堡基金。