Gradients des fonctions intérieures dans la boule unité de \({\mathbb{C}}^ n\). (Gradients of inner functions in the unit ball of \({\mathbb{C}}^ n)\) (Q1070063)
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scientific article; zbMATH DE number 3933435
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gradients des fonctions intérieures dans la boule unité de \({\mathbb{C}}^ n\). (Gradients of inner functions in the unit ball of \({\mathbb{C}}^ n)\) |
scientific article; zbMATH DE number 3933435 |
Statements
Gradients des fonctions intérieures dans la boule unité de \({\mathbb{C}}^ n\). (Gradients of inner functions in the unit ball of \({\mathbb{C}}^ n)\) (English)
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1986
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Inner functions in the unit ball of \({\mathbb{C}}^ n\) have always gradients in \(L^*_ 1\) but never in \(L_ 2\). Refining Aleksandrov's method we solve a problem of W. Rudin, to prove the existence of an inner function with gradient in \(L_ 1\).
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Inner functions in the unit ball of \({\mathbb{C}}^ n\)
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gradient
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