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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Gaussians never extremize Strichartz inequalities for hyperbolic paraboloids
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by Emanuel Carneiro, Lucas Oliveira and Mateus Sousa PDF
Proc. Amer. Math. Soc. 150 (2022), 3395-3403 Request permission


For $\xi = (\xi _1, \xi _2, \ldots , \xi _d) \in \mathbb {R}^d$ let $Q(\xi ) \colonequals \sum _{j=1}^d \sigma _j \xi _j^2$ be a quadratic form with signs $\sigma _j \in \{\pm 1\}$ not all equal. Let $S \subset \mathbb {R}^{d+1}$ be the hyperbolic paraboloid given by $S = \big \{(\xi , \tau ) \in \mathbb {R}^{d}\times \mathbb {R}\ : \ \tau = Q(\xi )\big \}$. In this note we prove that Gaussians never extremize an $L^p(\mathbb {R}^d) \to L^{q}(\mathbb {R}^{d+1})$ Fourier extension inequality associated to this surface.
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Additional Information
  • Emanuel Carneiro
  • Affiliation: ICTP - The Abdus Salam International Centre for Theoretical Physics, Strada Costiera, 11, I - 34151, Trieste, Italy
  • MR Author ID: 847171
  • ORCID: 0000-0001-6229-1139
  • Email:
  • Lucas Oliveira
  • Affiliation: Department of Pure and Applied Mathematics, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91509-900, Brazil
  • MR Author ID: 882219
  • Email:
  • Mateus Sousa
  • Affiliation: Mathematisches Institut der Universität München, Theresienstr. 39, D-80333 München, Germany; and BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain
  • MR Author ID: 1273391
  • ORCID: 0000-0002-1748-1803
  • Email:
  • Received by editor(s): January 24, 2020
  • Received by editor(s) in revised form: August 5, 2021
  • Published electronically: April 29, 2022
  • Additional Notes: The first author was partially supported by FAPERJ - Brazil
  • Communicated by: Alexander Iosevich
  • © Copyright 2022 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 150 (2022), 3395-3403
  • MSC (2020): Primary 42B10, 58E35
  • DOI:
  • MathSciNet review: 4439462