Restriction estimates for hyperbolic paraboloids in higher dimensions via bilinear estimates

Abstract

Let H be a .d 1/-dimensional hyperbolic paraboloid in R d and let Ef be the Fourier extension operator associated to H, with f supported in B d 1 .0; 2/. We prove that kEf k L p .B.0;R// Ä C " R " kf k L p for all p 2.d C 2/=d whenever d=2 m C 1, where m is the minimum between the number of positive and negative principal curvatures of H. Bilinear restriction estimates for H proved by S. Lee and Vargas play an important role in our argument.