Restriction for homogeneous polynomial surfaces in \(\mathbb R^3\) (Q2838069)
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scientific article; zbMATH DE number 6185152
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Restriction for homogeneous polynomial surfaces in \(\mathbb R^3\) |
scientific article; zbMATH DE number 6185152 |
Statements
8 July 2013
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Fourier restriction
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vanishing Gaussian curvature
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homogeneous polynomial
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Littlewood-Paley theorem
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Restriction for homogeneous polynomial surfaces in \(\mathbb R^3\) (English)
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The authors are concerned with analogs of the Stein-Tomas restriction theorem for surfaces whose Gaussian curvature may vanish. After P. Sjölin, it is usual to compensate for the possibly vanishing curvature with a mitigating factor. Since known estimates of decay for the Fourier transform of the measure supported on the surface do not work, the authors use a special method. A key ingredient in the proof is a Littlewood-Paley type theorem for homogeneous polynomials. The elaborated method is really effective only for dimension three. The paper is long and quite technical.
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