A convolution estimate for two-dimensional hypersurfaces
Ioan Bejenaru
University of Chicago, United StatesSebastian Herr
Universität Bielefeld, GermanyDaniel Tataru
University of California, Berkeley, USA
![A convolution estimate for two-dimensional hypersurfaces cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rmi-volume-26-issue-2.png&w=3840&q=90)
Abstract
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.
Cite this article
Ioan Bejenaru, Sebastian Herr, Daniel Tataru, A convolution estimate for two-dimensional hypersurfaces. Rev. Mat. Iberoam. 26 (2010), no. 2, pp. 707–728
DOI 10.4171/RMI/615