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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     author = {N. A. Il'yasov},
     title = {On the {Order} of {Decrease} of {Uniform} {Moduli} of {Smoothness} for the {Classes} of {Functions} $E_{p,m}[\epsilon]$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {519--536},
     publisher = {mathdoc},
     volume = {78},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a3/}
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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/