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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
- Comments (When Available)

**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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