The Tomas–Stein inequality under the effect of symmetries
Abstract:
We prove new Fourier restriction estimates to the unit sphere $\mathbb{S}^{d-1}$ on the class of $O(d−k) \times O(k)$-symmetric functions, for every $d \ge 4$ and $2 \le k \le d-2$. As an application, we establish the existence of maximizers for the endpoint Tomas–Stein inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp in the Tomas–Stein regime.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsmonat/-jahr | 06.2021 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000134152 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 31 S. |
| Serie | CRC 1173 Preprint ; 2021/27 |
| Projektinformation | SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019) |
| Externe Relationen | Siehe auch |
| Schlagwörter | Tomas–Stein inequality, Sharp Fourier Restriction Theory, symmetry, orthogonal group, maximizers, maximizing sequences |