Rational approximation of functions of several variables with finite Hardy variation

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
$$R_n(f,[0,1]^N)\leqslant C\frac{\ln^2 n}n\,.$$