Boundary values of harmonic gradients and differentiability of Zygmund and Weierstrass functions
type: Item
instance of: scholarly article
title: Boundary values of harmonic gradients and differentiability of Zygmund and Weierstrass functions
zbMATH Open document ID: 1298.31002
DOI: 10.4171/RMI/806
author: Artur Nicolau
author: Juan Jesús Donaire
author: José G. Llorente
published in: Revista Matemática Iberoamericana
publication date: 2014-10-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1202.0147
review text: Summary: 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.
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 31B25
Mathematics Subject Classification ID: 26B05
zbMATH DE Number: 6353616
zbMATH Keywords: harmonic functions
zbMATH Keywords: Zygmund class
zbMATH Keywords: Weierstrass functions
zbMATH Keywords: Hausdorff dimension
MaRDI profile type: Publication
arXiv ID: 1202.0147
cites work: Probabilistic Behaviour of Functions in the Zygmund Spaces ∧ * and λ *
cites work: Q5503905
cites work: Q5849097
cites work: The boundary correspondence under quasiconformal mappings
cites work: On the existence of boundary values for harmonic functions in several variables
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description: scientific article; zbMATH DE number 6353616