English

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.

Keywords

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}
}
R2 v1 2026-06-21T16:59:37.164Z