  We establish asymptotic estimates for exact upper bounds of uniform
approximations by Fourier sums on the classes of $2\pi$-periodic functions,
which are represented by convolutions of functions $\varphi (\varphi\bot 1)$
from unit ball of the space $L_{1}$ with fixed kernels $\Psi_{\beta}$ of the
form $\Psi_{\beta}(t)=\sum\limits_{k=1}^{\infty}\psi(k)
\cos\left(kt-\frac{\beta\pi}{2}\right)$,
$\sum\limits_{k=1}^{\infty}k\psi(k)<\infty$, $\psi(k)\geq 0$,
$\beta\in\mathbb{R}$.
