The Hardy-Littlewood maximal function of a Sobolev function (Q1366942)
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scientific article; zbMATH DE number 1062358
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Hardy-Littlewood maximal function of a Sobolev function |
scientific article; zbMATH DE number 1062358 |
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The Hardy-Littlewood maximal function of a Sobolev function (English)
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17 September 1997
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In this paper a main result is that the Hardy-Littlewood maximal operator is bounded in the Sobolev space \(W^{1,p}(\mathbb{R}^n)\) for \(1<p\leq\infty\). This result is applied to study a weak type inequality for the Sobolev capacity and to prove that the Hardy-Littlewood maximal function of a Sobolev function is quasi-continuous.
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quasi-continuity
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Hardy-Littlewood maximal operator
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Sobolev space
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Sobolev capacity
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Hardy-Littlewood maximal function
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