Linear methods for approximation of some classes of holomorphic functions from the Bergman space - Savchuk, V. V. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
We construct a linear method of the approximation $ \{Q_{n,ψ} \}_{n \in {\mathbb 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 $ψ(z) = \sum^∞_{k=0}ψ_k z^k.$ We give conditions on $ψ$ under which the method$ \{Q_{n,ψ} \}_{n \in {\mathbb 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.