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 language | English |
|---|---|
| Pages (from-to) | 1-22 |
| Number of pages | 22 |
| Journal | Journal of Geometric Analysis |
| DOIs | |
| Publication status | Accepted/In press - Jun 20 2017 |
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
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Cite this
Castro, A. J., Llorente, J. G., & Nicolau, A. (Accepted/In press). Oscillation of Generalized Differences of Hölder and Zygmund Functions. Journal of Geometric Analysis, 1-22. https://doi.org/10.1007/s12220-017-9882-4