We construct a linear method {ie910-01} for the approximation (in the unit disk) of classes of holomorphic functions {ie910-02} that are the Hadamard convolutions of the unit balls of the Bergman space A p with reproducing kernels {ie910-03}. We give conditions for ψ under which the method {ie910-04} approximates the class {ie910-05} in the metrics of the Hardy space H s and the Bergman space A s , 1 ≤ s ≤ p, with an error that coincides in order with the value of the best approximation by algebraic polynomials.
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Translated from in Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 6, pp. 783–795, June, 2008.
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Savchuk, V.V. Linear methods for approximation of some classes of holomorphic functions from the Bergman space. Ukr Math J 60, 910–926 (2008). https://doi.org/10.1007/s11253-008-0104-x
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DOI: https://doi.org/10.1007/s11253-008-0104-x