2025京师调和分析论坛(5) (2025.9.26)
会议安排
Zoom会议号：885 326 62481，入会密码：111111
时间 |
报告人 |
报告题目 |
单位 |
21:00-21:45 |
Tuomas Hytönen |
New Characterizations of Sobolev Spaces (I) |
Aalto University, Finland |
21:50-22:35 |
New Characterizations of Sobolev Spaces (II) |
本会议由以下项目支持:
北京师范大学优秀青年创新团队项目“调和分析及其在偏微分方程中的应用”
北京师范大学教育部&科技部“调和分析及其应用创新引智基地”
国家自然科学基金重点项目“相关于球平均、Chirp函数和区域上算子的函数空间公理化实变理论及其应用”
会议组委会： 袁文(本次会议组织者), 戴峰, 杨大春, 张阳阳, 周渊
2025年9月22日
报告信息
报告人: Tuomas Hytönen (Aalto University, Finland)
报告题目: New Characterizations of Sobolev Spaces
报告摘要: The "defect", that the fractional Sobolev norm of order 0<s<1, fails to converge to the first-order Sobolev norm as s approaches 1, is a source of two types of substitute results: (1) characterisations of constant functions by integral conditions obtained by naive substitution of s=1 into the formula of the fractional Sobolev norm, and (2) derivative-free characterisations of the first-order Sobolev norm by suitable modifications of the said formula. In this talk, I will discuss extensions of both types of results for the versions of these function spaces over any complete doubling metric measure space supporting a Poincaré inequality. A key tool of independent interest is a new "macroscopic" Poincaré inequality, whose right-hand side has oscillations of the same form as the left-hand side, but at a smaller macroscopic scale 0<r<R, instead of an infinitesimal scale, where r approaches 0. Besides intrinsic interest, these results are motivated by applications to quantitative compactness properties of commutators [T, f] of singular integrals and pointwise multipliers.
