Gaussians never extremize Strichartz inequalities for hyperbolic paraboloids

Carneiro, Emanuel; Oliveira, Lucas und Sousa, Mateus (2022): Gaussians never extremize Strichartz inequalities for hyperbolic paraboloids. In: Proceedings of the American Mathematical Society, Bd. 150, Nr. 8: S. 3395-3403

Abstract

For xi = (xi(1), xi(2), ... , xi(d)) is an element of R-d let Q(xi) := Sigma(d)(j=1) sigma(j)xi(2)(j) be a quadratic form with signs sigma(j) is an element of {+/- 1} not all equal. Let S subset of Rd+1 be the hyperbolic paraboloid given by S = {(xi, tau) is an element of R-d x R : tau = Q(xi)}. In this note we prove that Gaussians never extremize an L-p(R-d) -> L-q(Rd+1) Fourier extension inequality associated to this surface.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 0002-9939
• Sprache: Englisch