Oscillation of Generalized Differences of Hölder and Zygmund Functions
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Springer
Abstract
We analyze the oscillation of functions with Hölder or Zygmund regularity via generalized differences and show that its growth obeys a variant of Kolmogorov’s Law of the Iterated Logarithm. A sharper behavior is obtained for Lipschitz functions through a connection with Calderón–Zygmund operators.
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Castro, A.J.; Llorente, J.G.; Nicolau, A. (2018). Oscillation of Generalized Differences of Hölder and Zygmund Functions. Journal of Geometric Analysis, 28(2), 1–22. DOI: 10.1007/s12220-017-9882-4