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ISSN 1079-6762

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

Author(s): Jonathan Bennett
Journal: Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 97-102.
MSC (2000): Primary 42B10
Posted: August 31, 2004
MathSciNet review: 2084469
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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.

References:

1.: J. A. Barceló, J. M. Bennett, and A. Carbery, A multilinear extension inequality in $\mathbb{R}^{n}$ , Bull. London Math. Soc. 36 (3) (2004), 407-412. MR 2038728
2.: J. M. Bennett, A. Carbery, and J. Wright, A generalisation of the Loomis-Whitney inequality in $\mathbb{R}^{n}$ , in preparation.
3.: A. Moyua, A. Vargas, L. Vega, Restriction theorems and maximal operators related to oscillatory integrals in $\mathbb{R}^{3}$ , Duke Math. J. 96 (3) (1999), 547-574. MR 1671214 (2000b:42017)
4.: E. M. Stein, Harmonic Analysis, Princeton University Press, Princeton, NJ, 1993. MR 1232192 (95c:42002)
5.: T. Tao, A. Vargas, L. Vega, A bilinear approach to the restriction and Kakeya conjectures, J. Amer. Math. Soc. 11 (1998), 967-1000. MR 1625056 (99f:42026)

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Additional Information:

Jonathan Bennett
Affiliation: School of Mathematics, JCMB, Kings Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland
Email: J.Bennett@ed.ac.uk

DOI: 10.1090/S1079-6762-04-00134-9
PII: S 1079-6762(04)00134-9
Keywords: Multilinear estimates, Fourier extension operator
Received by editor(s): December 18, 2003
Posted: August 31, 2004
Additional Notes: The author was supported by an EPSRC Postdoctoral Fellowship.
Communicated by: Yitzhak Katznelson
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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