Approximations of classes of generalized Poisson integrals by Fourier sums in metrics of spaces $L_{s}$

TL;DR

This paper derives asymptotic bounds for the approximation of generalized Poisson integrals by Fourier sums within various $L_s$ spaces, focusing on functions in the unit ball of $L_1$, enhancing understanding of approximation quality.

Contribution

It provides new asymptotic equalities for approximation bounds of generalized Poisson integrals in $L_s$ spaces, extending previous results to a broader class of functions.

Findings

Established asymptotic equalities for approximation bounds

Extended approximation results to all $L_s$ spaces, $1 \\leq s \\leq \infty$

Focused on functions within the unit ball of $L_1$

Abstract

In metrics of spaces $L_{s}, \ 1\leq s\leq\infty$, we find asymptotic equalities for upper bounds of approximations by Fourier sums on classes of generalized Poisson integrals of periodic functions, which belong to unit ball of space $L_{1}$.