

Preprint 115/2002
A Rough Lipschitz Function
Bernd Kirchheim and Paul F. X. Müller
Contact the author: Please use for correspondence this email.
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.