On the exactness of certain inequalities in approximation theory

We prove the following: for every sequence $\{F_\nu\}$, $F_\nu\downarrow0$, $F_\nu>0$ there exists a function $
\begin{array}{l} 1)~E_n(f)\leqslant F_n\quad(n=0,1,2,\dots) \text{ и }\\ 2)~A_kn^{-k}\sum_{\nu=1}^n\nu^{k-1}F_{\nu-1}\leqslant\omega_k(f,n^{-1})\quad(n=1,2,\dots). \end{array}
$