Lebesgue-type inequalities for the de la Valee-Poussin sums on sets of analytic functions

  • A. P. Musienko Iн-т математики НАН України, Київ
  • A. S. Serdyuk

Abstract

For functions from the sets $C^{ψ}_{β} C$ and $C^{ψ}_{β} L_s,\; 1 ≤ s ≤ ∞$ generated by sequences $ψ(k) > 0$ satisfying the d’Alembert condition $\lim_{k→∞}\frac{ψ(k + 1)}{ψ(k)} = q,\; q ∈ (0, 1)$, we obtain asymptotically unimprovable estimates for the deviations of de la Vallee Poussin sums in the uniform metric in terms of the best approximations of the $(ψ, β)$-derivatives of functions of this sort by trigonometric polynomials in the metrics of the spaces $L_s$. It is proved that the obtained estimates are unimprovable in some important functional subsets of $C^{ψ}_{β} C$ and $C^{ψ}_{β} L_s$.
Published
25.04.2013
How to Cite
MusienkoA. P., and SerdyukA. S. “Lebesgue-Type Inequalities for the De La Valee-Poussin Sums on Sets of Analytic Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 4, Apr. 2013, pp. 522-37, http://umj.imath.kiev.ua/index.php/umj/article/view/2436.
Section
Research articles