2026京师调和分析论坛(5) (2026.8.21)
会议安排
Zoom会议号： 810 518 72359，入会密码：999999
时间 |
报告人 |
报告题目 |
单位 |
20:30-21:15 |
Tuomas Hytönen |
A-infinity-invariance of oscillatory norms, and Schatten characterisations of commutators (I) |
芬兰Aalto大学 |
21:25-22:10 |
A-infinity-invariance of oscillatory norms, and Schatten characterisations of commutators (II) |
会议由以下项目支持:
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”
组委会：戴峰, 杨大春, 袁文, 张阳阳
2026年8月17日
报告信息
报告题目: A-infinity-invariance of oscillatory norms, and Schatten characterisations of commutator
报告摘要: Schatten class properties of commutators [b,T] of pointwise multipliers b and singular integral operators T have been characterised in a variety of settings. An abstract framework, covering many of these results as special cases, was recently proposed by the speaker. However, more recent results about commutators of the concrete Bessel-Riesz transforms by Fan-Li-Sukochev-Zanin are beyond this abstract setting.
In this work, we present an extension of the original abstract framework by introducing two measures μ and ν that are A∞-equivalent to each other. The commutators act on a given space with measure μ, but the characterizing function space norms of the multiplier b are taken with respect to another measure ν. In this way, assumptions like Ahlfors regularity and Poincaré inequality on the original measure μ may be relaxed, as long as there is an A∞-equivalent measure ν that satisfies these assumptions. In the Bessel example, the original μ fails to be Ahlfors regular, but ν is simply the Lebesgue measure.
Within this framework, the Schatten norm characterisations of commutators of the Bessel-Riesz transforms at the critical-index by Fan-LiSukochev-Zanin are recovered by a completely different argument, replacing non-commutative techniques by real-variable harmonic analysis and hardly using any specifics of the Bessel setting. As a by-product, we also obtain a simpler characterisation in the non-critical case, replacing an ad-hoc Besov space of Fan-Lacey-Li-Xiong [J. Funct. Anal. 2026] by a classical Besov space.
