Geodesic
Rational approximations of absolutely continuous functions with derivative in an Orlicz space
Sbornik. Mathematics, Tome 45 (1983) no. 1, pp. 121-137

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Let $R_n(f)$ be the best uniform approximation of $f \in C[0,1]$ by rational fractions of degree at most $n$, and let $ W[0,1]$ be the set of monotone convex functions $w\in C[0,1]$ such that $w(0)=0$ and $w(1)=1$. Theorem 1. Suppose the function $f$ is absolutely continuous on the interval $[0,1],$ and let $w\in W[0,1]$ and $\widehat f= f(w(x))$. If $|\widehat f'|\ln^+|\widehat f'|$ is summable on $[0,1],$ then $R_n(f)=o(1/n)$. Various applications and generalizations of this result are given, and the periodic case is also considered. Bibliography: 23 titles. 
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     author = {A. A. Pekarskii},
     title = {Rational approximations of absolutely continuous functions with derivative in an {Orlicz} space},
     journal = {Sbornik. Mathematics},
     pages = {121--137},
     publisher = {mathdoc},
     volume = {45},
     number = {1},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_45_1_a7/}
}
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A. A. Pekarskii. Rational approximations of absolutely continuous functions with derivative in an Orlicz space. Sbornik. Mathematics, Tome 45 (1983) no. 1, pp. 121-137. http://geodesic.mathdoc.fr/item/SM_1983_45_1_a7/