Geodesic
Uniform rational approximations of functions of class~$V_r$
Sbornik. Mathematics, Tome 36 (1980) no. 3, pp. 389-403

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Let $V_r$ denote the set of functions $f$, defined on a finite interval $[a,b]$, for which $f^{(r-1)}$ is absolutely continuous on $[a,b]$ and is a primitive of a function of bounded variation; let $R_n(f)$ denote the best uniform approximation of $f$ by rational functions of order $n$. It is shown that $R_n(f)=o(n^{-r-1})$ for every $f\in V_r$ $(r\geqslant1)$, and that this estimate is of best possible order for the class $V_r$. Bibliography: 13 titles. 
@article{SM_1980_36_3_a6,
     author = {P. P. Petrushev},
     title = {Uniform rational approximations of functions of class~$V_r$},
     journal = {Sbornik. Mathematics},
     pages = {389--403},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {1980},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1980_36_3_a6/}
}
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P. P. Petrushev. Uniform rational approximations of functions of class~$V_r$. Sbornik. Mathematics, Tome 36 (1980) no. 3, pp. 389-403. http://geodesic.mathdoc.fr/item/SM_1980_36_3_a6/