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.
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