Differentiability of functions in the Zygmund class

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Abstract

Let f be a function in the Zygmund class in the euclidean space. It is proved that the Hausdorff dimension of the set of points where f has bounded divided differences, is bigger or equal to one. Furthermore, if f is in the Small Zygmund class, then the Hausdorff dimension of the set of points where f is differentiable, is bigger or equal to one. The sharpness of these results is also discussed. © 2013 London Mathematical Society.
Original languageEnglish
Pages (from-to)133-158
JournalProceedings of the London Mathematical Society
Volume108
DOIs
Publication statusPublished - 1 Jan 2014

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