# About function which Fourier coefficients satisfy $a_n=o(n^{-2}), b_n=o(n^{-2})$

Assume that a function $f: R\rightarrow R$ is $2 \pi$ -periodic and integrable on $[ -\pi,\pi]$. Let $(a_n)$, $(b_n)$ are its Fourier coefficients and $n^2 a_n, n^2 b_n \rightarrow 0$. Then by Weierstrass test $f$ is continuous. What we can say yet about $f$ (differentiability, continuously differentiability, Lipschitz condition, etc.) ?

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books.google.it/… –  Siminore May 5 '12 at 11:32