Lebesgue-type inequalities for the de la Vallée-poussin sums on sets of entire functions

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

Abstract

For functions from the sets C ψ β L s , 1 ≤ s ≤ ∞, where ψ(k) > 0 and \( {\lim_{{k\to \infty }}}\frac{{\psi \left( {k+1} \right)}}{{\psi (k)}} \) , we obtain asymptotically sharp estimates for the norms of deviations of the de la Vallée-Poussin sums in the uniform metric represented in terms of the best approximations of the (ψ, β) -derivatives of functions of this kind by trigonometric polynomials in the metrics of the spaces L s . It is shown that the obtained estimates are sharp on some important functional subsets.
Published
25.05.2013
How to Cite
MusienkoA. P., and SerdyukA. S. “Lebesgue-Type Inequalities for the De La Vallée-Poussin Sums on Sets of Entire Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 5, May 2013, pp. 642–653, http://umj.imath.kiev.ua/index.php/umj/article/view/2448.
Section
Research articles