Approximation of functions of a complex variable by Fourier sums in orthogonal systems in $L_2$

The sharp inequalities of Jackson-Stechkin type inequalities between the best approximation $E_{n-s-1}(f^{(s)}) (s=\overline{0,r}, r\in\mathbb{N})$ of successive derivatives $f^{(s)} (s=\overline{0,r}, r\in\mathbb{N})$ of analytic functions $f\in L_{2}(U)$ in the disk $U:=\left\{z: |z|<1\right\}$ as for special module of continuity $\Omega_{m}$ of $m$th order satisfying the condition
$$\Omega_{m}\left(f^{(r)},t\right)_{2}\leq\Phi(t), 0<t<1,$$
where $\Phi$ is give majorant and also for Peetre $\mathscr{K}$-functional satisfying the constraint
$$\mathscr{K}_{m}\left(f^{(r)},t^{m}\right)\leq\Phi(t^{m}), 0<t<1,$$
were obtained.