Existence of Extremals for a Fourier Restriction Inequality on the One-Sheeted Hyperboloid

We prove the existence of functions that extremize the endpoint L 2 to L 4 adjoint Fourier restriction inequality on the one-sheeted hyperboloid in Euclidean space R 4 and that, taking symmetries into consideration, any extremizing sequence has a subsequence that converges to an extremizer.

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Bibliographische Detailangaben
Veröffentlicht in:	The Journal of fourier analysis and applications 2024-08, Vol.30 (4), Article 44
1. Verfasser:	Quilodrán, René
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Approximations and Expansions Euclidean geometry Fourier Analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial Differential Equations Signal,Image and Speech Processing
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Beschreibung
Zusammenfassung:	We prove the existence of functions that extremize the endpoint L 2 to L 4 adjoint Fourier restriction inequality on the one-sheeted hyperboloid in Euclidean space R 4 and that, taking symmetries into consideration, any extremizing sequence has a subsequence that converges to an extremizer.
ISSN:	1069-5869 1531-5851
DOI:	10.1007/s00041-024-10090-2