Mathematical Research Letters

Volume 12 (2005)

Number 4

A non-linear generalisation of the Loomis-Whitney inequality andapplications

Pages: 443 – 457

DOI: http://dx.doi.org/10.4310/MRL.2005.v12.n4.a1

Authors

Jonathan Bennett

Anthony Carbery

James Wright

Abstract

We establish a diffeomorphism-invariant generalisation of the classical Loomis-Whitney inequality in $\RR^{n}$. As a consequence we obtain a sharp trilinear restriction theorem for the Fourier transform in three dimensions.

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