Abstract:
The paper continues the study of the rate of convergence of the group of deviations of rectangular sums of double trigonometric Fourier series, begun in [5]. The aim of the present article is to extend the results of [5] to the so-called generalized $L_p$-Hölder spaces $H_{\omega,p}\left( {{T}^{2}} \right)$, $1\le p\le \infty $, on the one hand, and to establish two-dimensional analogues of the author's results [7] regarding the approximation properties of the group of deviations in generalized $L_p$-Hölder spaces of functions of one variable, on the other hand.
The estimates established in the paper are of an ordinal nature and are formulated in terms of quantities defining the spaces $H_{\omega,p}\left( {{T}^{2}}\right) \subset H_{\omega^*,p}\left( {{T}^{2}}\right)$, and sequences $\alpha$ defining the corresponding groups of deviations.
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