题目: On entangled and multi-parameter commutators

报告人： 李康伟教授 天津大学

时间：2024年12月4日19:00-20:00

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摘要: 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.

简介：李康伟，国家级高层人才。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-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，2019年12月至今在天津大学工作。已在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。