Approximating Characteristics of the Nikol’skii–Besov Classes S1,θrBℝd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {S}_{1,\theta}^rB\left({\mathrm{\mathbb{R}}}^d\right) $$\end{document}

We establish the exact-order estimates for the approximation of the classes S1,θrBℝd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {S}_{1,\theta}^rB\left({\mathrm{\mathbb{R}}}^d\right) $$\end{document} by entire functions of exponential type such that the supports of their Fourier transforms lie in a step hyperbolic cross. The error of approximation is estimated in the metric of the Lebesgue space Lq(ℝd), 1 < q ≤  ∞ .