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Complex Analysis and Geometry Seminar

An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains

Liding Yao (U. Wisconsin-Madison) 

Location:  Zoom
Date & time: Friday, 04 March 2022 at 10:30AM - 11:30AM

Abstract: Given a bounded Lipschitz domain D in R^n, Rychkov showed that there is a linear extension operator E for D which is bounded in Besov and Triebel-Lizorkin spaces. In this talk, we introduce several new properties and estimates of the extension operator E and give some applications. In particular, we prove an equivalent norm property for general Besov and Triebel-Lizorkin spaces, which appears to be a well-known result but lacks a complete and correct proof to our best knowledge. We also derive some quantitative smoothing estimates of the extended function in \(overline{D}^c\) up to boundary. This is joint work with Ziming Shi. 

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