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Title: Approximation of Derivatives of Analytic Functions from One Hardy Class by Another Hardy Class
Authors: Akopyan, R. R.
Issue Date: 2020
Publisher: Pleiades journals
Pleiades Publishing Ltd
Citation: Akopyan R. R. Approximation of Derivatives of Analytic Functions from One Hardy Class by Another Hardy Class / R. R. Akopyan // Proceedings of the Steklov Institute of Mathematics. — 2020. — Vol. 308. — P. 1-8.
Abstract: In the Hardy space Hp(Dϱ), 1 ≤ p ⪯ ∞, of functions analytic in the disk Dϱ = {z ∈ ℂ}: z < ϱ, we denote by NHp(Dϱ), N > 0, the class of functions whose Lp-norm on the circle γϱ = {z ∈ ℂ: z = ϱ} does not exceed the number N and by ∂Hp(Dϱ) the class consisting of the derivatives of functions from 1Hp(Dϱ). We consider the problem of the best approximation of the class ∂Hp(Dϱ) by the class NHp(DR)N > 0, with respect to the Lp-norm on the circle γr, 0 < r < ρ < R. The order of the best approximation as N → +∞ is found: (Formula presented.) In the case where the parameter N belongs to some sequence of intervals, the exact value of the best approximation and a linear method implementing it are obtained. A similar problem is considered for classes of functions analytic in annuli. © 2020, Pleiades Publishing, Ltd.
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85085381000
PURE ID: 12922046
ISSN: 0081-5438
metadata.dc.description.sponsorship: This work was supported by the Russian Foundation for Basic Research (project no. 18-01-00336) and by the Russian Academic Excellence Project (agreement no. 02.A03.21.0006 of August 27, 2013, between the Ministry of Education and Science of the Russian Federation and Ural Federal University).
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