Differentiability of functions in the Zygmund class
Classical Analysis and ODEs
2014-02-26 v1
Abstract
We prove that the Hausdorff dimension of the set of points where a function in the Zygmund class in the euclidean space has bounded divided differences, is bigger or equal to 1. A similar result for functions in the Small Zygmund class is also proved and an example is constructed to show that these results are sharp.
Cite
@article{arxiv.1012.3545,
title = {Differentiability of functions in the Zygmund class},
author = {Juan Jesus Donaire and Jose G. Llorente and Artur Nicolau},
journal= {arXiv preprint arXiv:1012.3545},
year = {2014}
}