A SHARPENED STRICHARTZ INEQUALITY FOR THE WAVE EQUATION

We disprove a conjecture of Foschi, regarding extremizers for the Strichartz inequality with data in the Sobolev space (H) over dot(1/2) x (H) over dot(-1/2)(R-d), for even d >= 2. On the other hand, we provide evidence to support the conjecture in odd dimensions and refine his sharp inequality in R1+3, adding a term proportional to the distance of the initial data from the set of extremizers. The proofs use the conformal compactification of the Minkowski space-time given by the Penrose transform.