A trilinear restriction problem for the paraboloid in $\mathbb {R}^{3}$
Author:
Jonathan Bennett
Journal:
Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 97-102
MSC (2000):
Primary 42B10
DOI:
https://doi.org/10.1090/S1079-6762-04-00134-9
Published electronically:
August 31, 2004
MathSciNet review:
2084469
Full-text PDF Free Access
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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.
- J. A. Barceló, J. M. Bennett, and A. Carbery, A multilinear extension inequality in $\Bbb R^n$, Bull. London Math. Soc. 36 (2004), no. 3, 407–412. MR 2038728, DOI 10.1112/S0024609304003091
bcw J. M. Bennett, A. Carbery, and J. Wright, A generalisation of the Loomis–Whitney inequality in $\mathbb {R}^{n}$, in preparation.
- A. Moyua, A. Vargas, and L. Vega, Restriction theorems and maximal operators related to oscillatory integrals in $\mathbf R^3$, Duke Math. J. 96 (1999), no. 3, 547–574. MR 1671214, DOI 10.1215/S0012-7094-99-09617-5
- Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
- Terence Tao, Ana Vargas, and Luis Vega, A bilinear approach to the restriction and Kakeya conjectures, J. Amer. Math. Soc. 11 (1998), no. 4, 967–1000. MR 1625056, DOI 10.1090/S0894-0347-98-00278-1
BBC2 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.
bcw J. M. Bennett, A. Carbery, and J. Wright, A generalisation of the Loomis–Whitney inequality in $\mathbb {R}^{n}$, in preparation.
MVV 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.
St E. M. Stein, Harmonic Analysis, Princeton University Press, Princeton, NJ, 1993.
TVV T. Tao, A. Vargas, L. Vega, A bilinear approach to the restriction and Kakeya conjectures, J. Amer. Math. Soc. 11 (1998), 967–1000.
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Additional Information
Jonathan Bennett
Affiliation:
School of Mathematics, JCMB, Kings Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland
MR Author ID:
625531
Email:
J.Bennett@ed.ac.uk
Keywords:
Multilinear estimates,
Fourier extension operator
Received by editor(s):
December 18, 2003
Published electronically:
August 31, 2004
Additional Notes:
The author was supported by an EPSRC Postdoctoral Fellowship.
Communicated by:
Yitzhak Katznelson
Article copyright:
© Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
