On \(H^\infty\)-disks attached to completely real manifolds (Q1387380)
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scientific article; zbMATH DE number 1158940
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(H^\infty\)-disks attached to completely real manifolds |
scientific article; zbMATH DE number 1158940 |
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On \(H^\infty\)-disks attached to completely real manifolds (English)
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4 June 1998
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The main theorem of this note is: Let \(M\) be a completely real manifold of class \(C^k\), \(k>1\), and let the mapping \(\Phi: U= \{z:| z| <1\} \to \mathbb{C}^n\) be an \(H^\infty\)-disk attached to \(M\). Then either \(\Phi\in C^{k-0} (\overline U)\) or the area of the disk \(\Phi (U)\) is infinite. This result is the generalization of the Frostman theorem about inner functions.
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\(H^\infty\)-disk
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completely real manifold
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