Editor's note: the differentiability of functions in \({\mathbb{R}}^ n\) (Q788243)
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scientific article; zbMATH DE number 3842495
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Editor's note: the differentiability of functions in \({\mathbb{R}}^ n\) |
scientific article; zbMATH DE number 3842495 |
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Editor's note: the differentiability of functions in \({\mathbb{R}}^ n\) (English)
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1981
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The following theorem is proven: suppose \(F:{\mathbb{R}}^ n\to {\mathbb{R}}\) be such that \(\nabla F\in L^{n,1}_{loc}\) in the distribution sense \((L^{n,1}\) being a Lorentz space). Then F is equivalent to a continuous function and differentiable a.e. The proof is based on a suitable new maximal inequality proven as a lemma.
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Lorentz space
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maximal inequality
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