# Seminars & Colloquia Calendar

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.

## Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.