  We obtain exact for order estimates of best uniform approximations and
uniform approximations by Fourier sums of classes of convolutions the periodic
functions belong to unit balls of spaces $L_{p}, \ {1\leq p<\infty}$, with
generating kernel $\Psi_{\beta}$, whose absolute values of Fourier coefficients
$\psi(k)$ are such that
$\sum\limits_{k=1}^{\infty}\psi^{p'}(k)k^{p'-2}<\infty$,
$\frac{1}{p}+\frac{1}{p'}=1$, and product $\psi(n)n^{\frac{1}{p}}$ can't tend
to nought faster than power functions.
