报 告 人：宋仁明 教授
报告题目：Approximate factorizations for non-symmetric jump processes
报告时间：2025年6月18日（周三）下午4:00
报告地点：泉山校区5号楼107
主办单位：数学研究院、数学与统计学院、科学技术研究院
报告人简介：
宋仁明，美国Illinois大学教授，1986年河北大学硕士毕业，1989年美国Florida大学博士毕业。访问过德国、法国、日本、韩国和台湾等国家和地区的20余所大学和研究所。从事随机过程和随机分析研究，在《Trans. Amer. Math. Soc.》、《Proc. London Math. Soc.》、《J. European Math. Soc》、《Math. Ann.》、《J. Funct. Anal.》、《Ann. Probab.》、《Probab. Th. Rel. Fields》、《Stoch. Proc. Appl.》等数学、概率国际权威刊物上发表论文160余篇；多次在国际学术会议上作邀请报告。
报告摘要：
In this talk, I will talk about a recent paper with Soobin Cho. In this paper, we first extend the approximate factorization for purely discontinuous Markov processes established by Cho-Kim-Song-Vondracek in 2020 by getting rid of some of the conditions. Then we apply the approximate factorization to obtain two-sided heat kernel estimates for three classes of processes: stable-like processes with stable killings in $C^{1, Dini}$ open sets; killed stable-like processes in the setting of the recent preprint by Kim-Weidner in $C^{1, \epsilon}$ open sets; and non-symmetric stable processes in what we call $C^{1, 2-Dini}$ open sets. In particular, we obtain explicit sharp two-sided heat kernel estimates of killed $\alpha$-stable processes in $C^{1, Dini}$ open sets for all $\alpha\in (0, 2)$ and of censored $\alpha$-stable processes in $C^{1, Dini}$ open sets for $\alpha\in (1, 2)$.