On Seeley-type Universal Extension Operators for the Upper Half Space
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910439025147904 |
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| author | Lu, Haowen Yao, Liding |
| author_facet | Lu, Haowen Yao, Liding |
| contents | 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 Hölder spaces, Besov and Triebel-Lizorkin spaces, along with their Morrey generalizations. We also give an analogous construction on bounded smooth domains. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_15567 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Seeley-type Universal Extension Operators for the Upper Half Space Lu, Haowen Yao, Liding Classical Analysis and ODEs Functional Analysis 46E35 (primary) and 46F10 (secondary) 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 Hölder spaces, Besov and Triebel-Lizorkin spaces, along with their Morrey generalizations. We also give an analogous construction on bounded smooth domains. |
| title | On Seeley-type Universal Extension Operators for the Upper Half Space |
| topic | Classical Analysis and ODEs Functional Analysis 46E35 (primary) and 46F10 (secondary) |
| url | https://arxiv.org/abs/2211.15567 |