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Multiple Fourier Series for Functions from a Zygmund Class / Donskikh S.L. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 1. P. 3-12 [Moscow Univ. Math. Bulletin. Vol. 65, No 1, 2010. P. 1-9]. The paper concerns with necessary and sufficient conditions providing that a function of many variables with nonnegative trigonometric Fourier coefficients velongs to the big and small Zygmund classes. Earler, such a result was obtained by R. P. Boas in the one-dimensional case and by V. Fülöp in the two-dimensional case.
Key words: functions of many variables, Fourier coefficients, Zygmund classes.
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