An improved bound for Kakeya type maximal functions (Q1907051)
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scientific article; zbMATH DE number 838780
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An improved bound for Kakeya type maximal functions |
scientific article; zbMATH DE number 838780 |
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An improved bound for Kakeya type maximal functions (English)
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22 February 1996
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In this fascinating paper the author establishes improved \(L^p\to L^q\) bounds for Kakeya and Besicovich type maximal functions. As one particular consequence of the estimates he obtains a new lower bound for the Hausdorff dimension \(\ell\) of the Kakeya set in \(\mathbb{R}^d\), namely \(\ell\geq (d+ 2)/2\).
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Kakeya maximal function
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Besicovich maximal function
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Hausdorff dimension
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Kakeya set
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