An In-depth Look at Rychkov's Universal Extension Operators for Lipschitz Domains
数学专题报告
报告题目(Title)：An In-depth Look at Rychkov's Universal Extension Operators for Lipschitz Domains
报告人(Speaker)：姚力丁 (美国俄亥俄州立大学)
地点(Place)：后主楼1124
时间(Time)：2023年6月29日(周四), 10:00-11:00
邀请人(Inviter)：杨大春、袁文
报告摘要
Given a bounded Lipschitz domain $\Omega\subset\mathbb R^n$, Rychkov showed that there is a linear extension operator $\mathcal E$ for $\Omega$ which is bounded in Besov and Triebel-Lizorkin spaces. In this paper we introduce some new estimates for the extension operator $\mathcal E$ and give some applications. We prove the equivalent norms $\|f\|_{\mathscrA_{pq}^s(\Omega)}\approx\sum_{|\alpha|\le m}\|\partial^\alpha f\|_{\mathscr A_{pq}^{s-m}(\Omega)}$ for general Besov and Triebel-Lizorkin spaces. We also derive some quantitative smoothing estimates of the extended function and all its derivatives in $\overline{\Omega}^c$ up to boundary. This is a joint work with Ziming Shi.
主讲人简介
姚力丁，俄亥俄州立大学博士后研究员，2022年博士毕业于威斯康星大学麦迪逊分校。研究方向是调和分析、多复变函数、函数空间及其应用，相关研究成果发表于获接受发表于Amer. J. Math., J. Funct. Anal., J. Fourier Anal. Appl., J. Geom. Anal., J. Anal. Math., Proc. Amer. Math. Soc.等学术期刊上。
