## Weierstrass functions in Zygmund’s class

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- by Yanick Heurteaux PDF
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**133**(2005), 2711-2720 Request permission

## Abstract:

Consider the function \[ f(x)=\sum _{n=0}^{+\infty }b^{-n}g(b^nx)\] where $b>1$ and $g$ is an almost periodic $C^{1,\varepsilon }$ function. It is well known that the function $f$ lives in the so-called Zygmund class. We prove that $f$ is generically nowhere differentiable. This is the case in particular if the elementary condition $g^\prime (0)\not = 0$ is satisfied. We also give a sufficient condition on the Fourier coefficients of $g$ which ensures that $f$ is nowhere differentiable.## References

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## Additional Information

**Yanick Heurteaux**- Affiliation: Laboratoire de Mathématiques, UMR 6620, Université Blaise Pascal, F-63177 Aubière cedex, France
- Email: Yanick.Heurteaux@math.univ-bpclermont.fr
- Received by editor(s): April 29, 2004
- Published electronically: March 22, 2005
- Communicated by: David Preiss
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**133**(2005), 2711-2720 - MSC (2000): Primary 26A27, 28A80
- DOI: https://doi.org/10.1090/S0002-9939-05-07857-3
- MathSciNet review: 2146218