\(L^ p\)-boundedness of the Hilbert transform and maximal function along flat curves in \(\mathbb{R}^ n\) (Q1901174)
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scientific article; zbMATH DE number 812635
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^ p\)-boundedness of the Hilbert transform and maximal function along flat curves in \(\mathbb{R}^ n\) |
scientific article; zbMATH DE number 812635 |
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\(L^ p\)-boundedness of the Hilbert transform and maximal function along flat curves in \(\mathbb{R}^ n\) (English)
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8 January 1996
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Hilbert transform and maximal function associated to a curve \(\Gamma (t)=\) \({(t, \gamma_2 (t), \dots, \gamma_n (t))}\) in \(\mathbb{R}^n\) are considered. It is well-known that for a plane convex curve \(\Gamma (t)= (t, \gamma (t))\) these operators are bounded on \(L^p\), \(1<p <\infty\), if \(\gamma'\) doubles. We give an \(n\)-dimensional analogue, \(n\geq 2\), of this result.
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flat curves
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Calderón-Zygmund theory
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Littlewood-Paley decompositions
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Hilbert transform
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maximal function
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