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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