Geodesic
On the Order of Decrease of Uniform Moduli of Smoothness for the Classes of Functions $E_{p,m}[\epsilon]$
Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 519-536.

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In this paper, we solve the problem of the exact order of decrease of uniform moduli of smoothness for the classes of $2\pi$-periodic functions of several variables with a given majorant of the sequence of total best approximations in the metric of $L_p$, $1\le p\infty$. 
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N. A. Il'yasov. On the Order of Decrease of Uniform Moduli of Smoothness for the Classes of Functions $E_{p,m}[\epsilon]$. Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 519-536. http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a3/

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