Approximation of Poisson integrals by one linear approximation method in uniform and integral metrics

We obtain asymptotic equalities for the least upper bounds of approximations of classes of Poisson integrals of periodic functions by a linear approximation method of special form in the metrics of the spaces C and L _p . Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 976–982, July, 2008.