Asymptotic behavior of best approximations of classes of infinitely differentiable functions defined by moduli of continuity

Abstract: We obtain asymptotic estimates for the best approximations by trigonometric polynomials in the metric space $C$ $(L_p)$ of classes of periodic functions that can be represented as a convolution of kernels $\Psi_\beta$, which Fourier coefficients tend to zero faster than any power sequence, with functions $\varphi\in C (\varphi\in L_p),$ which moduli of continuity do not exceed a fixed majorant $\omega(t)$. It is proved that in the spaces $C$ and $L_1$ the obtained estimates are asymptotically exact for convex moduli of continuity $\omega(t)$.