Journal of Fourier Analysis and Applications

, Volume 16, Issue 1, pp 17-33

First online:

Simple Proofs of Nowhere-Differentiability for Weierstrass’s Function and Cases of Slow Growth

  • Jon JohnsenAffiliated withDepartment of Mathematical Sciences, Aalborg University Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


Using a few basics from integration theory, a short proof of nowhere-differentiability of Weierstrass functions is given. Restated in terms of the Fourier transformation, the method consists in principle of a second microlocalisation, which is used to derive two general results on existence of nowhere differentiable functions. Examples are given in which the frequencies are of polynomial growth and of almost quadratic growth as a borderline case.


Nowhere-differentiability Weierstrass function Lacunary Fourier series Second microlocalisation

Mathematics Subject Classification (2000)