Differentiability of functions in the Zygmund class

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.

Cited by in corpus (4)

• Approximation in the Zygmund Class
• Central limit theorem for generalized Weierstrass functions
• Approximation in the Zygmund and Hölder classes on ${\mathbb{R}}^n$
• Existence of principal values of some singular integrals on Cantor sets, and Hausdorff dimension