Gaussians rarely extremize adjoint Fourier restriction inequalities for paraboloids

DOI10.1090/S0002-9939-2013-11827-7zbMath1285.26035arXiv1012.1346OpenAlexW2963653472MaRDI QIDQ5401670

René Quilodrán, Michael Christ

Publication date: 11 March 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.1346

zbMATH Keywords

Euler-Lagrange equationsStrichartz inequalitiesparaboloidGaussiansFourier restriction inequalitycritial pointsdilation-invariant measureradial Gaussian

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Inequalities for sums, series and integrals (26D15) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Related Items (15)

On existence of extremizers for the Tomas-Stein inequality for \(S^{1}\) ⋮ Extremizers for adjoint restriction to pairs of translated paraboloids ⋮ The maximal Strichartz family of Gaussian distributions: Fisher information, index of dispersion, and stochastic ordering ⋮ Some recent progress on sharp Fourier restriction theory ⋮ Gaussians never extremize Strichartz inequalities for hyperbolic paraboloids ⋮ Real analysis, harmonic analysis and applications. Abstracts from the workshop held July 3--9, 2022 ⋮ Extremizers for adjoint restriction to a pair of reflected paraboloids ⋮ On the extremizers of an adjoint Fourier restriction inequality ⋮ Extremizers for Fourier restriction on hyperboloids ⋮ A sharp 𝑘-plane Strichartz inequality for the Schrödinger equation ⋮ Extremizers for Fourier restriction inequalities: convex arcs ⋮ Extremizability of Fourier restriction to the paraboloid ⋮ Smoothness of solutions of a convolution equation of restricted type on the sphere ⋮ Sharp Strichartz inequalities for fractional and higher-order Schrödinger equations ⋮ Critical Points of Strichartz Functional

Cites Work

• Unnamed Item
• On the extremizers of an adjoint Fourier restriction inequality
• Heat-flow monotonicity of Strichartz norms
• Existence of extremals for a Fourier restriction inequality
• Maximizers for the Strichartz inequality
• On sharp Strichartz inequalities in low dimensions
• Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schr\"odinger equation

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