Web of Science: 10 cites, Scopus: 10 cites, Google Scholar: cites
Fourier restriction to convex surfaces of revolution in R3
Abi-Khuzam, Faruk
Shayya, Bassam

Data: 2006
Resum: If Γ is a C3 hypersurface in Rn and dσ is induced Lebesgue measure on Γ, then it is well known that a Tomas-Stein Fourier restriction estimate on Γ implies that Γ has a nowhere vanishing Gaussian curvature. In a recent paper, Carbery and Ziesler observed that if induced Lebesgue measure is replaced by affine surface area, then a Tomas-Stein restriction estimate on Γ implies that Γ satisfies the affine isoperimetric inequality. Since the only property needed for a hypersurface to satisfy the affine isoperimetric inequality is convexity, this raised the question of whether a TomasStein restriction estimate can be obtained for flat but convex hypersurfaces in Rn such as Γ(x) = (x, e−1/ $m ), m = 1, 2, . . . . We prove that this is indeed the case in dimension n = 3.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: Article ; recerca ; Versió publicada
Publicat a: Publicacions matemàtiques, V. 50 n. 1 (2006) p. 71-85, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/38264
DOI: 10.5565/PUBLMAT_50106_04

15 p, 178.5 KB

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