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.

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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 : $1\leq p<2$ 
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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/

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