Order estimates of the best approximations and approximations of Fourier sums of classes of convolutions of periodic functions of not high smoothness in uniform metric

Abstract: 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.