Multiple Fourier series for functions from a Zygmund class / S. L. Donskikh. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 1. P. 3-12 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. 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. Fulop in the two-dimensional case.

Key words: functions of many variables, Fourier coefficients, Zygmund classes.