An endpoint estimate of the bilinear paraboloid restriction operator

Abstract

In Fourier restriction problems, a cone and a paraboloid are model surfaces. The sharp bilinear cone restriction estimate was first shown by Wolff, and later the endpoint was obtained by Tao. For a paraboloid, the sharp $L^2$ bilinear restriction estimate was obtained by Tao, but the endpoint was remained open. In this paper we prove the endpoint $L^2$ bilinear restriction estimate for a paraboloid.

30 pages, 2 figures. The previous version has some discordant elements in section 8. We have corrected them

Cited by in corpus (1)

• A new approach to the Fourier extension problem for the paraboloid