Order estimates of the best orthogonal trigonometric approximations of classes of convolutions of periodic functions of not high smoothness

We obtain order estimates for the best uniform orthogonal trigonometric approximations of $2\pi$-periodic functions, whose $(\psi,\beta)$-derivatives belong to unit balls of spaces $L_{p}, \ 1\leq p<\infty$, in case at consequences $\psi(k)$ are that product $\psi(n)n^{\frac{1}{p}}$ can tend to zero slower than any power function and $\sum\limits_{k=1}^{\infty}\psi^{p'}(k)k^{p'-2}<\infty$ when $1