In the present work, we emphasize, for the first time, the error estimation of a two-variable function \(g(y,z)\) in the generalized Zygmund class \(Y_{r}^{(\xi )}\) (\(r\geq 1\)) using the double Hausdorff matrix means of its double Fourier series. In fact, in this work, we establish two theorems on error estimation of a two-variable function of g in the generalized Zygmund class.

中文翻译：

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双Hausdorff矩阵逼近广义Zygmund类中的函数。

在本工作中，我们首次强调广义Zygmund类\（Y_ {r} ^ {（\ xi）}中二元函数\（g（y，z）\）的误差估计\）（\（r \ geq 1 \））使用其双重傅里叶级数的双重Hausdorff矩阵表示。实际上，在这项工作中，我们建立了广义Zygmund类中g的两个变量函数的误差估计的两个定理。