报告题目：On entangled and multi-parameter commutators

报 告 人：李康伟

报告时间：2026年3月29日10：00

报告地点：2B408

报告人简介：李康伟，浙江师范大学教授、博士生导师，国家优秀青年科学基金获得者。从事调和分析方向的研究工作，主要包括小波分析、奇异积分算子理论及其加权理论。2015年6月于南开大学获博士学位。2015年至2019年先后在芬兰赫尔辛基大学、西班牙巴斯克应用数学中心从事博士后研究。已在Amer. J. Math., Adv. Math., Math. Ann., J. Math. Pures. Appl., IMRN, Trans. AMS, J. Funct. Anal.等国际知名期刊发表多篇论文。

内容简介：We complement the recent theory of general singular integrals $T$ invariant under the Zygmund dilations $(x_1, x_2, x_3) \mapsto (s x_1, tx_2, st x_3)$ by proving necessary and sufficient conditions for the boundedness and compactness of commutators $[b,T]$ from $L^p \to L^q$. Previously, only the $p=q$ upper bound in terms of a Zygmund type little BMO space was known for general operators, and there has been some confusion about the corresponding lower bound in recent literature. We give complete characterizations whenever $p \le q$ for a general class of non-degenerate Zygmund type singular integrals. Some of the results are surprising in view of existing papers, for instance, compactness always forces $b$ to be constant. Even in the simpler situation of bi-parameter singular integrals this has not been observed previously.