A convolution estimate for two-dimensional hypersurfaces

Details A convolution estimate for two-dimensional hypersurfaces A convolution estimate for two-dimensional hypersurfaces

2008-09-30

arxiv.org/abs/0809.5091v3

Rev. Mat. Iberoam. Vol. 26 No. 2, 707-728 (2010)

Mathematics

Analysis of PDEs

21 pages, 1 figure

Scientific paper

Given three transversal and sufficiently regular hypersurfaces in 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 R^3, under scaleable assumptions. The resulting uniform L^2 estimate has applications to nonlinear dispersive equations.

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