报告人：李康伟 （天津大学 研究员）
报告时间：2025年7月30日(周三)下午14:30
报告地点：集美大学理学院章辉楼447
联系人：郭炜超
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报告摘要：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.
报告人简介：李康伟，天津大学数学科学学院研究员，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，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.,Forum Math Sigma等国际知名期刊发表50多篇论文。
