  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.
