JournalsrmiVol. 30, No. 3pp. 1037–1071

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

  • Juan J. Donaire

    Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain
  • José G. Llorente

    Universitat Autònoma de Barcelona, Bellaterra, Spain
  • Artur Nicolau

    Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain
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Abstract

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.

Cite this article

Juan J. Donaire, José G. Llorente, Artur Nicolau, Boundary values of harmonic gradients and differentiability of Zygmund and Weierstrass functions. Rev. Mat. Iberoam. 30 (2014), no. 3, pp. 1037–1071

DOI 10.4171/RMI/806