Revista Matemática Iberoamericana


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Volume 30, Issue 3, 2014, pp. 1037–1071
DOI: 10.4171/RMI/806

Published online: 2014-08-27

Boundary values of harmonic gradients and differentiability of Zygmund and Weierstrass functions

Juan J. Donaire[1], José G. Llorente[2] and Artur Nicolau[3]

(1) Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain
(2) Universitat Autònoma de Barcelona, Bellaterra, Spain
(3) Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain

We study differentiability properties of Zygmund functions and series of Weierstrass type in higher dimensions. While such functions may be nowhere differentiable, we show that, under appropriate assumptions, the set of points where the incremental quotients are bounded has maximal Hausdorff dimension.

Keywords: Zygmund class, Weierstrass functions, Hausdorff dimension

Donaire Juan, Llorente José, Nicolau Artur: Boundary values of harmonic gradients and differentiability of Zygmund and Weierstrass functions. Rev. Mat. Iberoamericana 30 (2014), 1037-1071. doi: 10.4171/RMI/806