Abstract:
Questions dealing with the approximation of functions from the classes $C^{\psi}_{\beta}H^{\alpha}$ by Poisson integrals are studied. The Kolmogorov–Nikolskii problem for Poisson integrals for the classes $C^{\psi}_{\beta}H^{\alpha}$ is solved in the uniform metric.
Keywords:approximation of functions, the classes $C^{\psi}_{\beta}H^{\alpha}$, Poisson integral, Fourier series, Kolmogorov–Nikolskii problem, $(\psi,\beta)$-derivative.