New estimates of Rychkov's universal extension operator for Lipschitz domains and some applications

Abstract

Given a bounded Lipschitz domain , Rychkov showed that there is a linear extension operator for Ω, which is bounded in Besov and Triebel‐Lizorkin spaces. In this paper, we introduce some new estimates for the extension operator and give some applications. We prove the equivalent norms for general Besov and Triebel‐Lizorkin spaces. We also derive some quantitative smoothing estimates of the extended function and all its derivatives on up to the boundary.