Juan Jesus Donaire, Jose G. Llorente, Artur Nicolau
Published 2010-12-16Version 1
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.
On volumes determined by subsets of Euclidean space
On the Lebesgue measure, Hausdorff dimension, and Fourier dimension of sums and products of subsets of Euclidean space
Hausdorff dimension of level sets of generalized Takagi functions
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