Oscillation of Generalized Differences of Hölder and Zygmund Functions

Oscillation of Generalized Differences of Hölder and Zygmund Functions

In this paper we analyze the oscillation of functions having derivatives in the Hölder or Zygmund class in terms of generalized differences and prove that its growth is governed by a version of the classical Kolmogorov’s Law of the Iterated Logarithm. A better behavior is obtained for functions in t...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:The Journal of Geometric Analysis 2018-04, Vol.28 (2), p.1665-1686
Hauptverfasser: Castro, Alejandro J., Llorente, José G., Nicolau, Artur
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In this paper we analyze the oscillation of functions having derivatives in the Hölder or Zygmund class in terms of generalized differences and prove that its growth is governed by a version of the classical Kolmogorov’s Law of the Iterated Logarithm. A better behavior is obtained for functions in the Lipschitz class via an interesting connection with Calderón–Zygmund operators.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-017-9882-4