Geodesic
The sharp Jackson inequality in the space $L_2$ on the segment $[-1,1]$ with the power weight
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 112-126 
V. I. Ivanov; D. V. Chertova; Liu Yongping. The sharp Jackson inequality in the space $L_2$ on the segment $[-1,1]$ with the power weight. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 112-126. http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a9/
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     title = {The sharp {Jackson} inequality in the space $L_2$ on the segment $[-1,1]$ with the power weight},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the space $L_2$ on the segment $[-1,1]$ with the power weight $|x|^{2\lambda+1}$, $\lambda\ge-1/2$ , we define a complete orthogonal system, the value of the best approximation with respect to this system, the operator of generalized shift, and the modulus of continuity and prove the sharp Jackson inequality.

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