Small Cap Square Function Estimates

We introduce and prove small cap square function estimates for the unit parabola and the truncated light cone. More precisely, we study inequalities of the form ‖ f ‖ p ≤ C α , p ( R ) ‖ ( ∑ γ ∈ Γ α ( R - 1 ) | f γ | 2 ) 1 / 2 ‖ p , where Γ α ( R - 1 ) is the set of small caps of width R - α . We fi...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	The Journal of fourier analysis and applications 2024-06, Vol.30 (3), Article 36
1. Verfasser:	Gan, Shengwen
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Approximations and Expansions Estimates Fourier Analysis Lower bounds Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial Differential Equations Signal,Image and Speech Processing
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	We introduce and prove small cap square function estimates for the unit parabola and the truncated light cone. More precisely, we study inequalities of the form ‖ f ‖ p ≤ C α , p ( R ) ‖ ( ∑ γ ∈ Γ α ( R - 1 ) \| f γ \| 2 ) 1 / 2 ‖ p , where Γ α ( R - 1 ) is the set of small caps of width R - α . We find sharp upper and lower bounds of the constant C α , p ( R ) .
ISSN:	1069-5869 1531-5851
DOI:	10.1007/s00041-024-10095-x