A bilinear approach to the restriction and Kakeya conjectures

Details A bilinear approach to the restriction and Kakeya conjectures A bilinear approach to the restriction and Kakeya conjectures

1998-07-29

arxiv.org/abs/math/9807163v1

Mathematics

Classical Analysis and ODEs

33 pages, 3 figures, LaTeX, to appear JAMS

Scientific paper

Bilinear restriction estimates have been 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 $q > 4 - 5/27$.

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