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
DOI:
https://doi.org/10.1090/S0894-0347-98-00278-1
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
Email:
tao@math.ucla.edu
Ana Vargas
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Email:
ana.vargas@uam.es
Luis Vega
Affiliation:
Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain
MR Author ID:
237776
Email:
mtpvegol@lg.ehu.es
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