@article{906bef235ce24ecf91959471ce4b7ce6,
title = "Oscillation of Generalized Differences of H{\"o}lder and Zygmund Functions",
abstract = "In this paper we analyze the oscillation of functions having derivatives in the H{\"o}lder or Zygmund class in terms of generalized differences and prove that its growth is governed by a version of the classical Kolmogorov{\textquoteright}s Law of the Iterated Logarithm. A better behavior is obtained for functions in the Lipschitz class via an interesting connection with Calder{\'o}n–Zygmund operators.",
keywords = "Calder{\'o}n–Zygmund operators, Generalized differences, H{\"o}lder functions, Law of the iterated logarithm, Lipschitz functions, Martingales, Oscillation, Zygmund class",
author = "Castro, {Alejandro J.} and Llorente, {Jos{\'e} G.} and Artur Nicolau",
note = "Funding Information: The first author is partially supported by Spanish Government Grant MTM2016-79436-P. The last two authors are partially supported by the Generalitat de Catalunya, Grant 2014SGR 75, and the Spanish Ministerio de Econom?a, Grant MTM2014-51824-P. Funding Information: Acknowledgements The first author is partially supported by Spanish Government Grant MTM2016-79436-P. The last two authors are partially supported by the Generalitat de Catalunya, Grant 2014SGR 75, and the Spanish Ministerio de Econom{\'i}a, Grant MTM2014-51824-P. Publisher Copyright: {\textcopyright} 2017, Mathematica Josephina, Inc.",
year = "2017",
month = jun,
day = "20",
doi = "10.1007/s12220-017-9882-4",
language = "English",
volume = "28",
pages = "1--22",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer New York",
number = "2",
}