A characterization of compactness via bilinear T1 theorem
数学学科创建110周年系列报告
报告题目(Title)：A characterization of compactness via bilinear T1 theorem
报告人(Speaker)：曹明明 （哈尔滨工业大学）
地点(Place)：腾讯会议：703927582
时间(Time)：2025年6月13日（星期五），17:00-18:00
邀请人(Inviter)：薛庆营
报告摘要
The celebrated T1 theorem due to David and Journ\’{e} gives a necessary and sufficient condition for $L^2$ boundedness of singular integral operators $T$. This was extended by Villarroya in 2015 to obtain the compactness of $T$. However, the $T1$ theorem to deduce compactness of multilinear singular integrals has been an open problem for almost ten years. In this talk we solve this long standing problem. Our main approaches consist of the following new ingredients: (i) a resulting representation of a compact bilinear Calder\'{o}n--Zygmund operator as an average of some compact bilinear dyadic shifts and paraproducts; (ii) extrapolation of endpoint compactness for bilinear operators; and (iii) compactness criterion in weighted Lorentz spaces.
主讲人简介
曹明明，哈尔滨工业大学数学研究院教授，2023年获优秀青年基金项目(海外)。2018年毕业于北京师范大学，2019-2025年先后在西班牙国家科学院从事博士后工作和研究员(tenure track)。主要研究领域包括调和分析、偏微分方程、几何测度论，现已发表30多篇论文，包括Adv. Math, Math Ann, Forum Math Sigma, Trans. AMS, JFA等国际知名期刊。
