Order estimates of approximative characteristics of functions from   classes $S^{r}_{1,\theta}B(\mathbb{R}^d)$
  We obtained exact order estimates of approximation of the classes $S^{\boldsymbol{r}}_{1,\theta}B$ by entire functions of exponential type with supports of their Fourier transforms in step hyperbolic cross. The error of the approximation estimated in the metric of Lebesgue spaces, $L_q(\mathbb{R}^d)$, $1<q\leqslant \infty$. 
S. Ya. Yanchenko
math.CA