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June, 2010 A convolution estimate for two-dimensional hypersurfaces
Ioan Bejenaru , Sebastian Herr , Daniel Tataru
Rev. Mat. Iberoamericana 26(2): 707-728 (June, 2010).


Given three transversal and sufficiently regular hypersurfaces in $\mathbb{R}^3$ it follows from work of Bennett-Carbery-Wright that the convolution of two $L^2$ functions supported of the first and second hypersurface, respectively, can be restricted to an $L^2$ function on the third hypersurface, which can be considered as a nonlinear version of the Loomis-Whitney inequality. We generalize this result to a class of $C^{1,\beta}$ hypersurfaces in $\mathbb{R}^3$, under scaleable assumptions. The resulting uniform $L^2$ estimate has applications to nonlinear dispersive equations.


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Ioan Bejenaru . Sebastian Herr . Daniel Tataru . "A convolution estimate for two-dimensional hypersurfaces." Rev. Mat. Iberoamericana 26 (2) 707 - 728, June, 2010.


Published: June, 2010
First available in Project Euclid: 4 June 2010

zbMATH: 1203.42033
MathSciNet: MR2677013

Primary: 42B35
Secondary: 47B38

Keywords: $L^2$ estimate , convolution , Hypersurface , induction on scales , transversality

Rights: Copyright © 2010 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.26 • No. 2 • June, 2010
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