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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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