English

Oscillation of generalized differences of H\"older and Zygmund functions

Classical Analysis and ODEs 2023-10-25 v1 Probability

Abstract

In this paper we analyze the oscillation of functions having derivatives in the H\"older 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 Calder\'on-Zygmund operators.

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Cite

@article{arxiv.1610.08155,
  title  = {Oscillation of generalized differences of H\"older and Zygmund functions},
  author = {Alejandro J. Castro and José G. Llorente and Artur Nicolau},
  journal= {arXiv preprint arXiv:1610.08155},
  year   = {2023}
}

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16 pages