On some approximate properties of biharmonic Poisson integrals in the integral metric

Abstract

This paper is devoted to solving one of the extremal problems in the theory of approximation of functional classes by linear methods of summation of the Fourier series in the integral metric, namely, approximation of classes $L^{\psi}_{\beta, 1}$ by biharmonic Poisson integrals. As a result of the research, we have found the asymptotic equalities for the approximation values of classes of $(\psi, \beta)$-differentiable functions by biharmonic Poisson integrals, that is, have found solutions of the Kolmogorov-Nikol'skii problem for biharmonic Poisson integrals on classes $L^{\psi}_{\beta, 1}$ in the integral metric.