On the Estimate of Deviations of Partial Sums of a Multiple Fourier-Walsh Series of the Form S _(2j,..,2j)f(x) of a Function in the Metric L_1(Q_k).

摘要

In this paper, deviations of the partial sums of a multiple Fourier-Walsh series of a function in the metric L_1 (Q_k) on a dyadic group are investigated. This estimate plays an important role in the study of equivalent normalizations in this space by means of a difference, oscillation, and best approximation by polynomials in the Walsh system. The classical classical Besov space and its equivalent normalizations are set forth in the well-known monographs of Nikolsky S.M., Besov O.V., llyin V.P., Triebel H.; in the works of Kazakh scientists such as Amanov T.I., Mynbaev K.T., Otelbaev M.O., Smailov E.S.. The Besov spaces on the dyadic group and the Vilenkin groups in the one-dimensional case are considered in works by Ombe H., Bloom Walter R, Fournier J., Onneweer C.W., Weyi S., Jun Tateoka.