Geodesic
Multiple Fourier series for functions from a Zygmund class
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2010), pp. 3-12

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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. 
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     author = {S. L. Donskikh},
     title = {Multiple {Fourier} series for functions from a {Zygmund} class},
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S. L. Donskikh. Multiple Fourier series for functions from a Zygmund class. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2010), pp. 3-12. http://geodesic.mathdoc.fr/item/VMUMM_2010_1_a0/