Boundary values of harmonic gradients and differentiability of zygmund and weierstrass functions

Juan J. Donaire, José G. Llorente, Artur Nicolau

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1037-1071
JournalRevista Matematica Iberoamericana
Volume30
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Hausdorff dimension
  • Weierstrass functions
  • Zygmund class

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