Oscillation of Generalized Differences of Hölder and Zygmund Functions

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

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1 Citation (Scopus)

Abstract

© 2017, Mathematica Josephina, Inc. 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)1665-1686
JournalJournal of Geometric Analysis
Volume28
Issue number2
DOIs
Publication statusPublished - 1 Apr 2018

Keywords

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

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