Sobolev extension domains on metric spaces of homogeneous type. (Q595811)
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scientific article; zbMATH DE number 2083994
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sobolev extension domains on metric spaces of homogeneous type. |
scientific article; zbMATH DE number 2083994 |
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Sobolev extension domains on metric spaces of homogeneous type. (English)
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6 August 2004
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The author proves that there exists a bounded linear extension operator \[ \text{Ext}: M^{1,p}(\Omega,d,\mu)\to M^{1,p}(\Omega, d,\mu) \] such that \(\text{Ext}(u)|_\Omega= u\), where \(M^{1,p}(\Omega,d,\mu)\) is the Hajlasz space. Here, \((X,d,\mu)\) is a metric measure space of homogeneous type with a finite measure.
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extension operator
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metric spaces of homogeneous type
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