We establish the exact-order estimates for the approximation of the classes \( {S}_{1,\theta}^rB\left({\mathrm{\mathbb{R}}}^d\right) \) 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 L_q(ℝ^d), 1 < q ≤ ∞ .

中文翻译：

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Nikol'skii–Besov类S1，θrBℝd$$ {S} _ {1，\ theta} ^ rB \ left（{\ mathrm {\ mathbb {R}}} ^ d \ right）$$的近似特征

我们建立的确切顺序概算类的近似（{\ THETA 1，} ^ rB中\左（{\ mathrm {\ mathbb {R}}} ^ d \右）\ {S} _）\通过整个指数类型的函数，以使它们的傅里叶变换的支持位于阶梯双曲线交叉中。逼近的误差估计在度量勒贝格空间的大号_q（ℝ ^d），1 <  q  ≤∞。