报告题目: Criteria for weak-type properties of generalized singular integral operators with rough kernels

报告人:  秦默言 讲师 (北京师范大学)

报告摘要：

We establish a criterion for the limiting weak-type behavior property of generalized singular integral operators with rough kernels. The operators under consideration are of the form $T_{\Omega,K}f(x)=\text{p.v.}\int_{\mathbb{R}^n}\Omega(x-y)\,K(x,y)\,f(y)\,dy$. Assume that the kernel $\Omega$ belongs to $L\log L(\mathbb{S}^{n-1})$ and satisfies the standard cancellation condition, while the kernel $K$ satisfies suitable size and regularity assumptions. Under these hypotheses, we show that the limiting weak-type behavior of $T_{\Omega,K}$ follows from its weak-type $(1,1)$ boundedness. As applications of this criterion, we show that the limiting weak-type behavior property holds for several classical operators with rough kernels, including Calder\'on-Zygmund singular integral operator, Calder\'on commutator, higher-order Calder\'on commutator, as well as the corresponding maximal truncated operators.

报告人简介： 秦默言，北京师范大学数学科学学院讲师。2022年毕业于北京师范大学。主要从事调和分析中算子有界性、弱极限行为方面的研究，相关成果发表在Calc. Var. Partial Differential Equations、Proc. Roy. Soc. Edinburgh Sect. A等国际知名期刊上。

报告时间: 2026.4.16(周四) 下午 15:30-16:30

报告地点: 逸夫楼1537