## 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

## Abstract:

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.## References

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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: carneiro@ictp.it
**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: lucas.oliveira@ufrgs.br
**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: mcosta@bcamath.org
- 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: https://doi.org/10.1090/proc/15782
- MathSciNet review: 4439462