, Volume 238, Issue 2, pp 215-268

Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates

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Abstract.

Recently Wolff [25] obtained a nearly sharp \(L^2\) bilinear restriction theorem for bounded subsets of the cone in general dimension. We obtain the endpoint of Wolff's estimate and generalize to the case when one of the subsets is large. As a consequence, we are able to deduce some nearly-sharp \(L^p\) null form estimates.

Received: 24 September 1999 / in final form: 25 April 2000 / Published online: 4 May 2001