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

• Date: 2013
• Main Authors: Musienko, A. P., Serdyuk, A. S., Мусієнко, А. П., Сердюк, А. С.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2436
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...