Oscillation of generalized differences of Hölder and Zygmund functions
arXiv:1610.08155 · doi:10.1007/s12220-017-9882-4
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.
16 pages