On Seeley‐type universal extension operators for the upper half space

Abstract

Modified from the standard half‐space extension via the reflection principle, we construct a linear extension operator for the upper half space that has the form for . We prove that E is bounded in all ‐spaces, Sobolev and Hölder spaces, Besov and Triebel–Lizorkin spaces, along with their Morrey generalizations. We also give an analogous construction on bounded smooth domains.