Linear methods for approximation of some classes of holomorphic functions from the Bergman space
We construct a linear method of the approximation {Q_n,ψ }_n N in the unit disk of classes of holomorphic functions A^ψ_p that are the Hadamard convolutions of unit balls of the Bergman space A_p with reproducing kernels ψ(z) = ^∞_k=0ψ_k z^k. We give conditions on ψ under which the method {Q_n,ψ }_n N approximate the class A^ψ_p in metrics of the Hardy space H_s and Bergman space A_s, 1 ≤ s ≤ p, with error that coincides in order with a value of the best approximation by algebraic polynomials., number=6, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Savchuk, V. V., year=2008, month=Jun., pages=783–795