Geodesic
On the Sharpness of Jackson's Inequality in the Spaces~$L_p$ on the Half-Line with Power Weight
Matematičeskie zametki, Tome 98 (2015) no. 5, pp. 684-694

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

In the space $L_p$, $1\leq p2$, on the half-line with power weight, Jackson's inequality between the value of the best approximation of a function by even entire functions of exponential type and its modulus of continuity defined by means of a generalized shift operator is well known. The question of the sharpness of the inequality remained open. For the constant in Jackson's inequality, we obtain a lower bound, which proves its sharpness.
Keywords: Jackson's inequality, value of the best approximation, the space $L_p$, entire functions of exponential type, modulus of continuity, generalized shift operator, substochastic matrix, Hoeffding estimate.
Mots-clés : $1\leq p<2$ 
@article{MZM_2015_98_5_a3,
     author = {V. I. Ivanov},
     title = {On the {Sharpness} of {Jackson's} {Inequality} in the {Spaces~}$L_p$ on the {Half-Line} with {Power} {Weight}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {684--694},
     publisher = {mathdoc},
     volume = {98},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a3/}
}
TY  - JOUR
AU  - V. I. Ivanov
TI  - On the Sharpness of Jackson's Inequality in the Spaces~$L_p$ on the Half-Line with Power Weight
JO  - Matematičeskie zametki
PY  - 2015
SP  - 684
EP  - 694
VL  - 98
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a3/
LA  - ru
ID  - MZM_2015_98_5_a3
ER  - 
%0 Journal Article
%A V. I. Ivanov
%T On the Sharpness of Jackson's Inequality in the Spaces~$L_p$ on the Half-Line with Power Weight
%J Matematičeskie zametki
%D 2015
%P 684-694
%V 98
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a3/
%G ru
%F MZM_2015_98_5_a3
V. I. Ivanov. On the Sharpness of Jackson's Inequality in the Spaces~$L_p$ on the Half-Line with Power Weight. Matematičeskie zametki, Tome 98 (2015) no. 5, pp. 684-694. http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a3/