On extremizers for Strichartz estimates for higher order Schrödinger equations

Abstract

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Some recent progress on sharp Fourier restriction theory

“…In §2 we deal with noncompact surfaces, and discuss the cases of the paraboloid and the cone, where a full characterization of extremizers is known, and the cases of the hyperboloid and a quartic perturbation of the paraboloid, where extremizers fail to exist. Most of the material in this section is contained in the works [12,23,39,43,44]. In §3 we discuss the case of spheres.…”

Sharp Strichartz inequalities for fractional and higher-order Schrödinger equations

“…Convolution of singular measures is treated in much greater generality in the companion paper [32]. Lemma 3.2 is almost contained in [31,32], and we just indicate the necessary changes.…”

Extremizers for Fourier restriction on hyperboloids

“…We mention a few interesting works that deal with sharp Fourier restriction theory on spheres [11,12,14,15,20,22,39], paraboloids [2,10,13,23,37], and cones [6,7,34,36]. Perturbations of these manifolds have been considered in [17,27,30,31,32]. Sharp bilinear Fourier restriction theory is the subject of [4,5,26,33], whereas other instances of sharp Strichartz inequalities [3], sharp Sobolev-Strichartz inequalities [18] and sharp Airy-Strichartz inequalities [24,38] have been considered as well.…”