Geodesic
Rational approximation of functions of several variables with finite Hardy variation
Sbornik. Mathematics, Tome 186 (1995) no. 11, pp. 1599-1620 
A. P. Bulanov. Rational approximation of functions of several variables with finite Hardy variation. Sbornik. Mathematics, Tome 186 (1995) no. 11, pp. 1599-1620. http://geodesic.mathdoc.fr/item/SM_1995_186_11_a2/
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     author = {A. P. Bulanov},
     title = {Rational approximation of functions of several variables with finite {Hardy} variation},
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     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_11_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The rate of rational approximation of functions of $N$ variables with given modulus of continuity and bounded Hardy variation on the unit N-cube $[0,1]^N$ is considered. In particular, if a function $f(x)$ on $[0,1]^N$ has bounded Hardy variation and $f \in\operatorname{Lip}\alpha$, $0<\alpha<1$ then it can be seen from the central result of this paper that $$ R_n(f,[0,1]^N)\leqslant C\frac{\ln^2 n}n\,. $$

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