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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) (Lᵖ, Lᵖ) spherical restriction theorem of Wolff from p > 42 / 11 p > 42/11 to p > 34 / 9 p > 34/9, and also obtain a sharp (L p, L q) (Lᵖ, Lq) spherical restriction theorem for q > 4 − 5 27 q> 4 - 527.
Tao et al. (Thu,) studied this question.
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