APPROXIMATION OF DIFFERENTIATION OPERATORS BY BOUNDED LINEAR OPERATORS IN LEBESGUE SPACES ON THE AXIS AND RELATED PROBLEMS IN THE SPACES OF \((p,q)\)-MULTIPLIERS AND THEIR PREDUAL SPACES

APPROXIMATION OF DIFFERENTIATION OPERATORS BY BOUNDED LINEAR OPERATORS IN LEBESGUE SPACES ON THE AXIS AND RELATED PROBLEMS IN THE SPACES OF \((p,q)\)-MULTIPLIERS AND THEIR PREDUAL SPACES

We consider a variant \(E_{n,k}(N;r,r;p,p)\) of the four-parameter Stechkin  problem \(E_{n,k}(N;r,s;p,q)\) on the best approximation of differentiation operators of order \(k\) on the class of \(n\) times differentiable functions \((0<k<n)\) in Lebesgue spaces on the real axis. We discuss the...

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Bibliographic Details
Main Author: Vitalii V. Arestov
Format: Article
Language:English
Published: Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics 2023-12-01
Series:Ural Mathematical Journal
Subjects:
differentiation operator, stechkin's problem, kolmogorov inequality, \((p,q)\)-multiplier, predual space for the space of \((p,q)\)-multipliers
Online Access:https://umjuran.ru/index.php/umj/article/view/701
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Summary:We consider a variant \(E_{n,k}(N;r,r;p,p)\) of the four-parameter Stechkin  problem \(E_{n,k}(N;r,s;p,q)\) on the best approximation of differentiation operators of order \(k\) on the class of \(n\) times differentiable functions \((0<k<n)\) in Lebesgue spaces on the real axis. We discuss the state of research in this problem and related problems in the spaces of multipliers of Lebesgue spaces and their predual spaces. We give two-sided estimates for \(E_{n,k}(N;r,r;p,p)\). The paper is based on the author's talk at the S.B. Stechkin's International Workshop-Conference on Function Theory (Kyshtym, Chelyabinsk region, August 1–10, 2023).
ISSN:2414-3952

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