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A bilinear approach to the restriction and Kakeya conjectures

Authors: Terence Tao, Ana Vargas and Luis Vega
Journal: J. Amer. Math. Soc. 11 (1998), 967-1000
MSC (1991): Primary 42B10, 42B25
MathSciNet review: 1625056
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Abstract: Bilinear restriction estimates have appeared in work of Bourgain, Klainerman, and Machedon. In this paper we develop the theory of these estimates (together with the analogues for Kakeya estimates). As a consequence we improve the $(L^p,L^p)$ spherical restriction theorem of Wolff from $p > 42/11$ to $p > 34/9$, and also obtain a sharp $(L^p,L^q)$ spherical restriction theorem for $q> 4 - \frac {5}{27}$.

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Additional Information

Terence Tao
Affiliation: Department of Mathematics, University of California–Los Angeles, Los Angeles, California 90024
MR Author ID: 361755
ORCID: 0000-0002-0140-7641

Ana Vargas
Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Luis Vega
Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain
MR Author ID: 237776

Keywords: Restriction conjecture, bilinear estimates, Kakeya conjecture
Received by editor(s): February 20, 1998
Additional Notes: The second author was partially supported by the Spanish DGICYT (grant number PB94-149) and the European Commission via the TMR network (Harmonic Analysis).
Article copyright: © Copyright 1998 American Mathematical Society