Given periodic function $f\in C^{w}[0,1]$ with its Fourier series $f(x)=\sum\limits_{s=-\infty}^{\infty}f_{s}\exp(2\pi isx)$. What can one say about the asymptotic order of
$\sum_{s=-K}^{K}\left(\frac{s}{K}\right)^{q}f_{s}\exp(2\pi isx)$ for $q>w$ and $K\rightarrow\infty$? Is it just a constant?