On the Order of Decrease of Uniform Moduli of Smoothness for the Classes of Functions $E_{p,m}[\epsilon]$

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 $L_p$, $1\le p\lt \infty$.