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

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title = "Boundary values of harmonic gradients and differentiability of zygmund and weierstrass functions",

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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author = "Donaire, {Juan J.} and Llorente, {Jos{\'e} G.} and Artur Nicolau",

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AU - Donaire, Juan J.

AU - Llorente, José G.

AU - Nicolau, Artur

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N2 - 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.

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.

KW - Hausdorff dimension

KW - Weierstrass functions

KW - Zygmund class

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

M3 - Article

VL - 30

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JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

SN - 0213-2230

ER -

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

Abstract

Keywords

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