Geodesic
A trilinear restriction problem for the paraboloid in ℝ³
Bennett, Jonathan1
1 School of Mathematics, JCMB, Kings Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland
Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 97-102 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S1079-6762-04-00134-9

Bennett, Jonathan 1

1 School of Mathematics, JCMB, Kings Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland 
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Bennett, Jonathan. A trilinear restriction problem for the paraboloid in ℝ³. Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 97-102. doi: 10.1090/S1079-6762-04-00134-9

[1] Barceló, J. A., Bennett, J. M., Carbery, A. A multilinear extension inequality in ℝⁿ Bull. London Math. Soc. 2004 407 412

[2] Moyua, A., Vargas, A., Vega, L. Restriction theorems and maximal operators related to oscillatory integrals in 𝐑³ Duke Math. J. 1999 547 574

[3] Stein, Elias M. Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals 1993

[4] Tao, Terence, Vargas, Ana, Vega, Luis A bilinear approach to the restriction and Kakeya conjectures J. Amer. Math. Soc. 1998 967 1000

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