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

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

doi:https://doi.org/10.4171/rmi/806

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

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

Research output: Contribution to journal › Article › Research › peer-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 language	English
Pages (from-to)	1037-1071
Journal	Revista Matematica Iberoamericana
Volume	30
DOIs	https://doi.org/10.4171/rmi/806
Publication status	Published - 1 Jan 2014

Keywords

Hausdorff dimension
Weierstrass functions
Zygmund class

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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.",

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AU - Nicolau, Artur

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AB - 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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KW - Weierstrass functions

KW - Zygmund class

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JO - Revista Matematica Iberoamericana

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