# Seminars & Colloquia Calendar

Complex Analysis and Geometry Seminar

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

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.