Geodesic
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, Tome 9 (2023) no. 2, pp. 4-27

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $(0$ 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).
Keywords: differentiation operator, Stechkin's problem, Kolmogorov inequality, predual space for the space of $(p,q)$-multipliers.
Mots-clés : $(p,q)$-multiplier 
@article{UMJ_2023_9_2_a0,
     author = {Vitalii V. Arestov},
     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},
     journal = {Ural mathematical journal},
     pages = {4--27},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2023_9_2_a0/}
}
TY  - JOUR
AU  - Vitalii V. Arestov
TI  - 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
JO  - Ural mathematical journal
PY  - 2023
SP  - 4
EP  - 27
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UMJ_2023_9_2_a0/
LA  - en
ID  - UMJ_2023_9_2_a0
ER  - 
%0 Journal Article
%A Vitalii V. Arestov
%T 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
%J Ural mathematical journal
%D 2023
%P 4-27
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UMJ_2023_9_2_a0/
%G en
%F UMJ_2023_9_2_a0
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, Tome 9 (2023) no. 2, pp. 4-27. http://geodesic.mathdoc.fr/item/UMJ_2023_9_2_a0/