Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes H_ω_p in the metrics of the spaces L_p - Serdyuk, A. S.; Sokolenko, I. V. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
We obtain upper estimates for the least upper bounds of approximations of the classes of Poisson integrals of functions from H_ω_p for 1 ≤ p < ∞ by a certain linear method U_n^* in the metric of the space L_p. It is shown that the obtained estimates are asymptotically exact for р = 1: In addition, we determine the asymptotic equalities for the best approximations of the classes of Poisson integrals of functions from H_ω_1 in the metric of the space L_1 and show that, for these classes, the method U_n^* is the best polynomial approximation method in a sense of strong asymptotic behavior.