2017
Том 69
№ 9

# Approximation of classes of analytic functions by Fourier sums in the metric of the space $L_p$

Serdyuk A. S.

Abstract

Asymptotic equalities are established for upper bounds of approximants by Fourier partial sums in a metric of spaces $L_p,\quad 1 \leq p \leq \infty$ on classes of the Poisson integrals of periodic functions belonging to the unit ball of the space $L_1$. The results obtained are generalized to the classes of $(\psi, \overline{\beta})$-differentiable functions (in the Stepanets sense) that admit the analytical extension to a fixed strip of the complex plane.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 10, pp 1635-1651.

Citation Example: Serdyuk A. S. Approximation of classes of analytic functions by Fourier sums in the metric of the space $L_p$ // Ukr. Mat. Zh. - 2005. - 57, № 10. - pp. 1395–1408.

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