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

Simple proofs of nowhere-differentiability for Weierstrass's function and cases of slow growth