Geodesic
On approximation of $l$-smooth functions by rational functions in the integral metric
Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 235-240.

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In this paper it is proved that, roughly speaking, the rapidity of approximation of $l$-smooth functions of $n$ variables by rational functions that depend on parameters is the same in the integral metric as in the uniform metric. 
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L. D. Ivanov. On approximation of $l$-smooth functions by rational functions in the integral metric. Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 235-240. http://geodesic.mathdoc.fr/item/IM2_1972_6_1_a6/

[1] Vitushkin A. G., Otsenka slozhnosti zadachi tabulirovaniya, Fizmatgiz, M., 1959

[2] Shapiro H., “Some negative theorems of approximation theory”, Michigan Math. J., 11 (1964), 211–217 | DOI | MR | Zbl

[3] Lorentz G. G., “Metric entropy and approximation”, Bull. Amer. Math. Soc., 72 (1966), 903–937 | DOI | MR | Zbl

[4] Warren H. E., “Lower bounds for approximation by nonlinear manifolds”, Trans. Amer. Math. Soc., 133:1 (1968), 167–179 | DOI | MR