Geodesic
A bilinear approach to the restriction and Kakeya conjectures
Tao, Terence1 ; Vargas, Ana2 ; Vega, Luis3
1 Department of Mathematics, University of California–Los Angeles, Los Angeles, California 90024
2 Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
3 Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain
Journal of the American Mathematical Society, Tome 11 (1998) no. 4, pp. 967-1000

Voir la notice de l'article provenant de la source American Mathematical Society

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 $q> 4 - \frac {5}{27}$.
DOI : 10.1090/S0894-0347-98-00278-1

Tao, Terence 1 ; Vargas, Ana 2 ; Vega, Luis 3

1 Department of Mathematics, University of California–Los Angeles, Los Angeles, California 90024
2 Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
3 Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080, Bilbao, Spain 
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Tao, Terence; Vargas, Ana; Vega, Luis. A bilinear approach to the restriction and Kakeya conjectures. Journal of the American Mathematical Society, Tome 11 (1998) no. 4, pp. 967-1000. doi: 10.1090/S0894-0347-98-00278-1

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