Approximation of Poisson integrals by de la Valleé-Poussin sums in uniform and integral metrics
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 approximatio...
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| Date: | 2010 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2010
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2991 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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 $L_1$. |
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