Geodesic
Rational approximation with sign-sensitive weight
Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 715-725

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

For metrics of sign-sensitive weight, a generalization of the Jackson theorem and an analog of the Dolzhenko theorem on the estimate of the variation of a function in terms of its least rational deviations are obtained. In the same metric, two-sided estimates for rational deviations of the function $\operatorname{sign}x$ are given. 
@article{MZM_1996_60_5_a6,
     author = {A. K. Ramazanov},
     title = {Rational approximation with sign-sensitive weight},
     journal = {Matemati\v{c}eskie zametki},
     pages = {715--725},
     publisher = {mathdoc},
     volume = {60},
     number = {5},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a6/}
}
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A. K. Ramazanov. Rational approximation with sign-sensitive weight. Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 715-725. http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a6/