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

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

doi:10.4171/rmi/806

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

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

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Resum

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.

Idioma original	Anglès
Pàgines (de-a)	1037-1071
Revista	Revista Matematica Iberoamericana
Volum	30
DOIs	https://doi.org/10.4171/rmi/806
Estat de la publicació	Publicada - 1 de gen. 2014

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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.",

keywords = "Hausdorff dimension, Zygmund class, Weierstrass functions",

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

year = "2014",

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doi = "10.4171/rmi/806",

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AU - Donaire, Juan J.

AU - Nicolau, Artur

AU - Llorente, José G.

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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 - Zygmund class

KW - Weierstrass functions

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

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