报告人：蒋仁进教授（天津大学）
报告时间：2021年10月15日周五下午14：00-16：00
2021年10月22日周五下午14：00-16：00
报告地点：数学楼216
报告题目：Lectures on Riesz transform on manifolds and Dirichlet metric measure spaces
报告摘要：In this lecture, I shall report some progresses regarding the study of Riesz transform on manifolds and Dirichlet metric measure spaces. This lecture will be composed by the following sessions:
1. The L^p-boundedness of the Riesz transform for p>2, in the setting where heat kernel satisfies both upper and lower Gaussian estimates. Perturbation result will also be provided.
2. The L^p-boundedness of the Riesz transform for p>2, in the case of manifolds with several ends, where the lower Gaussian bound fails for the heat kernel. In this setting, some interesting facts regarding gluing operator will be provided.
3. The L^p-boundednessof theRiesz transform for 1 4. Localizations of the behavior of the Riesz transform, and remaining questions. 专家简介：蒋仁进，教授，天津大学应用数学中心。从事调和分析与度量几何交叉领域的研究。在调和分析及度量几何研究中，对调和函数、热核的正则性问题，Riesz变换有界性问题等做出重要贡献，解决了相关多个公开问题。成果发表于Adv. Math.、Comm. Pure Appl. Math.、J. Math. Pures. Appl.、Math. Ann.等期刊。曾获国家优青资助、并入选天津市中青年领军人才等计划.