A trilinear restriction problem for the paraboloid in $\mathbb{R}^{3}$

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A trilinear restriction problem for the paraboloid in $\mathbb{R}^{3}$

Jonathan Bennett

Abstract.

We establish a sharp trilinear inequality for the extension operator associated to the paraboloid in $\mathbb{R}^{3}$. Our proof relies on a recent generalisation of the classical Loomis--Whitney inequality.

Copyright 2004 American Mathematical Society
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Article Info

ERA Amer. Math. Soc. 10 (2004), pp. 97-102
Publisher Identifier: S 1079-6762(04)00134-9
2000 Mathematics Subject Classification. Primary 42B10
Key words and phrases. Multilinear estimates, Fourier extension operator
Received by editors December 18, 2003
Received by editors in revised form July 16, 2004
Posted on August 31, 2004
Communicated by Yitzhak Katznelson
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Jonathan Bennett

School of Mathematics, JCMB, Kings Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland

E-mail address: J.Bennett@ed.ac.uk

The author was supported by an EPSRC Postdoctoral Fellowship.

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