2025京师调和分析论坛(3) (2025.3.27)
会议安排
Zoom会议号：879 118 31002，入会密码：111111
时间 |
报告人 |
报告题目 |
单位 |
21:00-23:00 |
Tuomas Hytönen |
Schatten properties of commutators and equivalent Sobolev norms on metric spaces |
Aalto University, Finland |
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3月24日
报告信息
报告人: Tuomas Hytönen (Aalto University, Finland)
报告题目: Schatten properties of commutators and equivalent Sobolev norms on metric spaces
报告摘要: I will discuss quantitative compactness properties of commutators of singular integrals and pointwise multipliers,and their characterisation in terms of the membership of the multiplier function in different function spaces. The quantitative compactness is measured by so-called Schatten norms, which describe the rate of convergence of finite-dimensional approximations of the operator. For commutators, there is a curious cut-off phenomenon: for Schatten class parameters either above, or equal to, or below a dimensional threshold, the Schatten class membership (or its weak-type version at the threshold) of the commutator is characterised by the condition that the multiplier belongs either to a Besov space, or a Sobolev space, or the space of constant functions, respectively. Over the past few years, the original results of this type on the Euclidean space have been extended to many new settings by several authors. In a recent joint work with R. Korte, we obtain a general framework that covers, unifies, and further extends many of these results. Some implications can be proved in general spaces of homogenous type, while others require additional standard assumptions, like suitable Poincare inequalities. As a tool of independent interest, we also obtain new characterisations of Sobolev spaces in this setting.
