A bilinear approach to the restriction and Kakeya conjectures

Tao, Terence; Vargas, Ana; Vega, Luis

doi:10.1090/S0894-0347-98-00278-1

A bilinear approach to the restriction and Kakeya conjectures
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by Terence Tao, Ana Vargas and Luis Vega

J. Amer. Math. Soc. 11 (1998), 967-1000

DOI: https://doi.org/10.1090/S0894-0347-98-00278-1

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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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