Title: An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains
Speaker: Liding Yao (University of Wisconsin-Madison)
Abstract: Given a bounded Lipschitz domain \Omega in \R^n, Rychkov showed that there is a linear extension operator E for \Omega which is bounded in Besov and Triebel-Lizorkin spaces. In this talk, we introduce several new properties and estimates of the extension operator 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 outside the domain up to boundary. This is joint work with Ziming Shi.
[Note: Liding will be one of our ZAPs starting in the fall semester.]