Solution of the Kolmogorov-Nikol’skii problem for three-harmonic Poisson integrals on classes $C^{\psi}_{\beta,\infty}$

Abstract

We obtain asymptotic equalities for upper bounds of approximations by threeharmonic integrals of Poisson $P_{3}(\delta)$ in uniform metric on classes of continuous $2\pi$-periodic functions whose $(\psi,\beta)$-derivatives belong to the unit ball of the space $L_{\infty}$, in the case when the functions $\psi(t)$ tend to zero faster, then the function $t^{-3}$, which defines an order of the saturation of the method $P_{3}(\delta)$