Contribution to the isomorphic classification of Sobolev spaces \(L_{(k)}^p(\Omega) (1\leq p<\infty)\) (Q2760123)
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scientific article; zbMATH DE number 1684127
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Contribution to the isomorphic classification of Sobolev spaces \(L_{(k)}^p(\Omega) (1\leq p<\infty)\) |
scientific article; zbMATH DE number 1684127 |
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13 May 2003
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Sobolev spaces
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linear extension operator
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isomorphic Banach spaces
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Contribution to the isomorphic classification of Sobolev spaces \(L_{(k)}^p(\Omega) (1\leq p<\infty)\) (English)
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The authors prove that if \(\Omega\) is an open non-empty subset of \({\mathbb R}^n\) and \(1\leq p<\infty\) and \(k\in \mathbb N\) are such that there exists a linear extension operator from the Sobolev space \(L^p_{(k)}(\Omega):=W^{k,p}(\Omega)\) to \(W^{k,p}({\mathbb R}^n)\), then \(W^{k,p}(\Omega)\) is isomorphic to \(W^{k,p}({\mathbb R}^n)\) as a Banach space.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00063].
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