The purpose of this note is to discuss several results that have been obtained in the last
decade in the context of sharp adjoint Fourier restriction/Strichartz inequalities. Rather than …

We consider the cubic nonlinear Schrödinger (NLS) equation set on a two-dimensional box
of size $ L $ with periodic boundary conditions. By taking the large-box limit $ L\to\infty $ in …

In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz
inequalities for the Schr\" odinger equation in all dimensions based on the recent linear …

The adjoint Fourier restriction inequality of Tomas and Stein states that the mapping f↦ f σ ̂
is bounded from L 2 (S 2) to L 4 (ℝ 3). We prove that there exist functions that extremize this …

We give a necessary and sufficient condition for the precompactness of all optimizing
sequences for the Stein–Tomas inequality. In particular, if a well-known conjecture about the …

Let u:\mathbbR*\mathbbR^n→\mathbbC be the solution of the linear Schrödinger equation
iu_t+ Δ u= 0\\\, u (0, x)= f (x) In the first part of this paper, we obtain a sharp inequality for the …

A necessary and sufficient condition on the precompactness of extremal sequences for one-
dimensional α-Strichartz inequalities, equivalently α-Fourier extension estimates, is …

The adjoint Fourier restriction inequality for the sphere S2 states that if f∈ L2 (S2, σ) then
fσ̂∈ L4 (R3). We prove that all critical points f of the functional [Formula: see text] are …

We prove the existence of maximizers for Strichartz inequalities for the wave equation in
dimensions d≧3. Our approach follows the scheme given by Shao in 21 which obtains the …

Abstract The Tomas–Stein inequality or the adjoint Fourier restriction inequality for the
sphere S 1 states that the mapping f↦ f σ ˆ is bounded from L 2 (S 1) to L 6 (R 2). We prove …