### 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 language | English |
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Pages (from-to) | 133-158 |

Journal | Proceedings of the London Mathematical Society |

Volume | 108 |

DOIs | |

Publication status | Published - 1 Jan 2014 |

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## Cite this

Donaire, J. J., Llorente, J. G., & Nicolau, A. (2014). Differentiability of functions in the Zygmund class.

*Proceedings of the London Mathematical Society*,*108*, 133-158. https://doi.org/10.1112/plms/pdt016