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

Juan Jesús Donaire | Zendy; José G. Llorente | Zendy; Artur Nicolau | Zendy

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

Author(s) -

Juan Jesús Donaire,

José G. Llorente,

Artur Nicolau

Publication year - 2014

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/806

Subject(s) - mathematics , differentiable function , hausdorff dimension , bounded function , boundary (topology) , pure mathematics , harmonic function , mathematical analysis , dimension (graph theory) , quotient , harmonic , physics , quantum mechanics

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.

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