On Strichartz estimates from decoupling and applications

Strichartz estimates are derived from $\ell^2$-decoupling for phase functions satisfying a curvature condition. Bilinear refinements without loss in the high frequency are discussed. Estimates are established from uniform curvature generalizing Galilean invariance or from transversality in one dimension. The bilinear refinements are utilized to prove local well-posedness for generalized cubic nonlinear Schr\"odinger equations

Nonexistence of extremals for the adjoint restriction inequality on the hyperboloid

We study the problem of existence of extremizers for the $L^2$ to $L^p$ adjoint Fourier restriction inequalities on the hyperboloid in dimensions 3 and 4, in which cases $p$ is an even integer. We will use the method developed by Foschi to show that extremizers do not exist.Comment: 32 pages. Correction for Theorem 1.2 and Proposition 7.5 and addition of Remark 1.