On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$

A solution of the problem on the exact order of deviation in the uniform metric of partial cubic sums of multiple trigonometric Fourier series on classes of functions with a given majorant for the total modulus of smoothness of the $l$th order in $L_1(\mathbb{T}^{m}) $ is presented, where $l\in \mathbb{N}$, $m\geq 1$.