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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     author = {L. D. Ivanov},
     title = {On approximation of $l$-smooth functions by rational functions in the integral 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/