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arXiv · 2211.15567

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

Haowen Lu·Liding Yao
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Abstract

Modified from the standard half-space extension via reflection principle, we construct a linear extension operator for the upper half space $\Bbb R^n_+$ that has the form $Ef(x)=\sum_{j=-\infty}^\infty a_jf(x',-b_jx_n)$ for $x_n<0$. We prove that $E$ is bounded in all $C^k$-spaces, Sobolev and H\"older spaces, Besov and Triebel-Lizorkin spaces, along with their Morrey generalizations. We also give an analogous construction on bounded smooth domains.

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Haowen Lu, Liding Yao. 2022-11-28. On Seeley-type Universal Extension Operators for the Upper Half Space. https://doi.org/10.1002/mana.202200551

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