Oscillation of Generalized Differences of Hölder and Zygmund Functions

Alejandro J. Castro, José G. Llorente, Artur Nicolau

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalJournal of Geometric Analysis
DOIs
Publication statusAccepted/In press - Jun 20 2017

Fingerprint

Oscillation
Lipschitz Class
Law of the Iterated Logarithm
Derivative
Operator
Class

Keywords

  • Calderón–Zygmund operators
  • Generalized differences
  • Hölder functions
  • Law of the iterated logarithm
  • Lipschitz functions
  • Martingales
  • Oscillation
  • Zygmund class

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Oscillation of Generalized Differences of Hölder and Zygmund Functions. / Castro, Alejandro J.; Llorente, José G.; Nicolau, Artur.

In: Journal of Geometric Analysis, 20.06.2017, p. 1-22.

Research output: Contribution to journalArticle

Castro, Alejandro J. ; Llorente, José G. ; Nicolau, Artur. / Oscillation of Generalized Differences of Hölder and Zygmund Functions. In: Journal of Geometric Analysis. 2017 ; pp. 1-22.
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