Global and local smoothness of the Hilbert transforms

Global and local smoothness of the Hilbert transforms

We study the smoothness properties of the Hilbert transform in terms of the smoothness of the function itself. We prove global and local analogues of Privalov’s theorem. The sharpness of these results is shown.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Proceedings of the Steklov Institute of Mathematics 2013-04, Vol.280 (1), p.169-180
Hauptverfasser: Dyachenko, Mikhail I., Nursultanov, Erlan D., Tikhonov, Sergey Yu
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We study the smoothness properties of the Hilbert transform in terms of the smoothness of the function itself. We prove global and local analogues of Privalov’s theorem. The sharpness of these results is shown.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543813010112