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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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
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/701 |
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| author | Vitalii V. Arestov |
| author_facet | Vitalii V. Arestov |
| author_sort | Vitalii V. Arestov |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-a45b52a8e86844979d2ea73f091a0169 |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | 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 |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-a45b52a8e86844979d2ea73f091a01692025-08-20T03:56:58ZengUral 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 MechanicsUral Mathematical Journal2414-39522023-12-019210.15826/umj.2023.2.001184APPROXIMATION 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 SPACESVitalii V. Arestov0Ural Federal University, 51 Lenin ave., Ekaterinburg, 620075We 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).https://umjuran.ru/index.php/umj/article/view/701differentiation operator, stechkin's problem, kolmogorov inequality, \((p,q)\)-multiplier, predual space for the space of \((p,q)\)-multipliers |
| spellingShingle | Vitalii V. Arestov 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 Ural Mathematical Journal differentiation operator, stechkin's problem, kolmogorov inequality, \((p,q)\)-multiplier, predual space for the space of \((p,q)\)-multipliers |
| title | 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| topic | differentiation operator, stechkin's problem, kolmogorov inequality, \((p,q)\)-multiplier, predual space for the space of \((p,q)\)-multipliers |
| url | https://umjuran.ru/index.php/umj/article/view/701 |
| work_keys_str_mv | AT vitaliivarestov approximationofdifferentiationoperatorsbyboundedlinearoperatorsinlebesguespacesontheaxisandrelatedproblemsinthespacesofpqmultipliersandtheirpredualspaces |