永利欢乐娱人城最新版下载 - 永利欢乐娱人城

2026京师调和分析论坛(5) (2026.8.21)

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永利欢乐娱人城最新版下载永利欢乐娱人城最新版下载部&科技部“调和分析及其应用创新引智基地”

永利欢乐娱人城最新版下载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” 继续了解

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. 同类内容

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.