Geodesic
Optimal Arguments in Jackson's Inequality in the Power-Weighted Space~$L_2(\mathbb{R}^d)$
Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 338-348

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

This paper is devoted to the determination of the optimal arguments in the exact Jackson inequality in the space $L_2$ on the Euclidean space with power weight equal to the product of the moduli of the coordinates with nonnegative powers. The optimal arguments are studied depending on the geometry of the spectrum of the approximating entire functions and the neighborhood of zero in the definition of the modulus of continuity. The optimal arguments are obtained in the case where the first skew field is a $l_p^d$-ball for $1\le p \le 2$, and the second is a parallelepiped.
Keywords: Jackson's inequality, power-weighted space $L_2(\mathbb{R}^d)$, modulus of continuity, skew field, Dunkl transform, Logan's problem, Hölder's inequality. 
@article{MZM_2013_94_3_a2,
     author = {A. V. Ivanov and V. I. Ivanov},
     title = {Optimal {Arguments} in {Jackson's} {Inequality} in the {Power-Weighted} {Space~}$L_2(\mathbb{R}^d)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {338--348},
     publisher = {mathdoc},
     volume = {94},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a2/}
}
TY  - JOUR
AU  - A. V. Ivanov
AU  - V. I. Ivanov
TI  - Optimal Arguments in Jackson's Inequality in the Power-Weighted Space~$L_2(\mathbb{R}^d)$
JO  - Matematičeskie zametki
PY  - 2013
SP  - 338
EP  - 348
VL  - 94
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a2/
LA  - ru
ID  - MZM_2013_94_3_a2
ER  - 
%0 Journal Article
%A A. V. Ivanov
%A V. I. Ivanov
%T Optimal Arguments in Jackson's Inequality in the Power-Weighted Space~$L_2(\mathbb{R}^d)$
%J Matematičeskie zametki
%D 2013
%P 338-348
%V 94
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a2/
%G ru
%F MZM_2013_94_3_a2
A. V. Ivanov; V. I. Ivanov. Optimal Arguments in Jackson's Inequality in the Power-Weighted Space~$L_2(\mathbb{R}^d)$. Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 338-348. http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a2/