A Rough Lipschitz Function

Bernd Kirchheim and Paul F. X. Müller

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Submission date: 22. Dec. 2002
Pages: 13
published in: Proceedings of the American Mathematical Society, 136 (2008) 11, p. 3875-3881 
DOI number (of the published article): 10.1090/S0002-9939-08-09322-2
Bibtex
with the following different title: A rough differentiable function
MSC-Numbers: 26A16, 30D55, 26A24, 30C99
Keywords and phrases: radial variation, beta-numbers
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Abstract:
A real-valued Lipschitz function on the unit interval is constructed such that

holds for every . Here measures the distance of f to the best approximating linear functions at scale around x.

This problem is linked to the ongoing efforts to provide geometric understanding for J. Bourgain's results that there exist points at which bounded harmonic functions have finite radial variation.