Given three transversal and sufficiently regular hypersurfaces in it follows from work of Bennett-Carbery-Wright that the convolution of two functions supported of the first and second hypersurface, respectively, can be restricted to an 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 hypersurfaces in , under scaleable assumptions. The resulting uniform 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. Iberoam. 26 (2010), no. 2, pp. 707–728DOI 10.4171/RMI/615