On Seeley-type Universal Extension Operators for the Upper Half Space

Abstract

Modified from the standard half-space extension via reflection principle, we construct a linear extension operator for the upper half space ${\mathbb{R}}_{+}^n$ that has the form $Ef(x)={\sum }_{j=-\infty }^{\infty }{a}_{j}f(x^{\prime },-b_j{x}_n)$ for $x_n<0$. We prove that $E$ is bounded in all $C^k$-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.

Final version; 19 pages, 1 figure. Appeared in Mathematische Nachrichten

References in corpus (2)

• Interpolation of Morrey-Campanato and Related Smoothness Spaces
• Anisotropic Lizorkin--Triebel Spaces with Mixed Norms --- Traces on Smooth Boundaries

Cited by in corpus (1)

• Sobolev and Hölder estimates for homotopy operators of the $\overline{\partial }$-equation on convex domains of finite multitype