Приближение интегралов Пуассона суммами Балле Пуссена в равномерной и интегральных метриках

Abstract

On classes of the Poisson integrals of functions belonging to the unit balls of the spaces Ls,1 ≤ s ≤ ∞, we establish asymptotic equalities for upper bounds of approximations by the Vallée Poussin sums in a uniform metric. Asymptotic equalities are obtained also for the case of approximation by the Vallée Poussin sums in metrics of the spaces Ls,1 ≤ s ≤ ∞, on classes of the Poisson integrals of functions belonging to the unit ball of the space L₁.

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 L₁.