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A characterization of compactness via bilinear T1 theorem
- 来源：
- 学校官网
- 收录时间：
- 2026-04-05 14:12:44
- 时间：
- 2023-11-13 16:10:00
- 地点：
- 七教7215
- 报告人：
- 曹明明
- 学校：
- 北京交通大学
- 关键词：
- T1 theorem, compactness, bilinear singular integrals, Calderón-Zygmund operators, dyadic shifts, paraproducts, weighted Lorentz spaces
- 简介：
- 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.
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报告介绍：
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.
报告人介绍：
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, Trans. AMS, JFA等国际知名期刊。
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