Приближение интегралов Пуассона суммами Балле Пуссена в равномерной и интегральных метриках

Анотація

On classes of the 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 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 $L_s , 1 ≤ s ≤ ∞$, on classes of the Poisson integrals of functions belonging to the unit ball of the space $L_1$.