Geodesic
Smoothness of functions and Fourier coefficients
Sbornik. Mathematics, Tome 210 (2019) no. 7, pp. 994-1018

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider functions represented as trigonometric series with general monotone Fourier coefficients. The main result of the paper is the equivalence of the $L_p$ modulus of smoothness, $1$, of such functions to certain sums of their Fourier coefficients. As applications, for such functions we give a description of the norm in the Besov space and sharp direct and inverse theorems in approximation theory. Bibliography: 34 titles.
Keywords: Fourier series, general monotone sequences, moduli of smoothness. 
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     author = {M. I. Dyachenko and A. B. Mukanov and S. Yu. Tikhonov},
     title = {Smoothness of functions and {Fourier} coefficients},
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     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_7_a2/}
}
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M. I. Dyachenko; A. B. Mukanov; S. Yu. Tikhonov. Smoothness of functions and Fourier coefficients. Sbornik. Mathematics, Tome 210 (2019) no. 7, pp. 994-1018. http://geodesic.mathdoc.fr/item/SM_2019_210_7_a2/