Restriction estimates for hyperbolic paraboloids in higher dimensions via bilinear estimates

Let \mathbb{H} be a (d-1) -dimensional hyperbolic paraboloid in \mathbb{R}^d and let Ef be the Fourier extension operator associated to \mathbb{H} , with f supported in B^{d-1}(0,2) . We prove that \lVert Ef \rVert_{L^p (B(0,R))} \leq C_{\varepsilon}R^{\varepsilon}\lVert f \rVert_{L^p} for all p \ge...

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Veröffentlicht in:Revista matemática iberoamericana 2022-01, Vol.38 (5), p.1453-1471, Article 1453
1. Verfasser: Barron, Alex
Format: Artikel
Sprache:eng
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Zusammenfassung:Let \mathbb{H} be a (d-1) -dimensional hyperbolic paraboloid in \mathbb{R}^d and let Ef be the Fourier extension operator associated to \mathbb{H} , with f supported in B^{d-1}(0,2) . We prove that \lVert Ef \rVert_{L^p (B(0,R))} \leq C_{\varepsilon}R^{\varepsilon}\lVert f \rVert_{L^p} for all p \geq 2(d+2)/d whenever d/2\geq m + 1 , where m is the minimum between the number of positive and negative principal curvatures of \mathbb{H} . Bilinear restriction estimates for \mathbb{H} proved by S. Lee and Vargas play an important role in our argument.
ISSN:0213-2230
2235-0616
DOI:10.4171/rmi/1310