Approximation of Poisson integrals by de la Valleé-Poussin sums in uniform and integral metrics

  • A. S. Serdyuk

Abstract

On the classes of Poisson integrals of functions belonging to the unit balls of the spaces $L_s , 1 ≤ s ≤ ∞$, we establish asymptotic equalities for upper bounds of approximations by de la Vallée-Poussin sums in the uniform metric. Asymptotic equalities are also obtained for the case of approximation by de la Vallée-Poussin sums in the metrics of the spaces $L_s , 1 ≤ s ≤ ∞$, on the classes of Poisson integrals of functions belonging to the unit ball of the space $L_1$.
Published
25.12.2010
How to Cite
Serdyuk, A. S. “Approximation of Poisson Integrals by De La Valleé-Poussin Sums in Uniform and Integral Metrics”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 12, Dec. 2010, pp. 1672–1686, https://umj.imath.kiev.ua/index.php/umj/article/view/2991.
Section
Research articles