Geodesic
On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 161-177

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

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 $l\in \mathbb{N}$, $m\geq 1$.
Keywords: multiple trigonometric Fourier series, partial cubic sums, order of uniform convergence, total modulus of smoothness, exact order of deviation in the uniform metric. 
@article{TIMM_2015_21_4_a15,
     author = {N. A. Il'yasov},
     title = {On the order of the uniform convergence of partial cubic sums of multiple trigonometric {Fourier} series on the function classes $H_{1,m}^{l}[\omega]$},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {161--177},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a15/}
}
TY  - JOUR
AU  - N. A. Il'yasov
TI  - On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2015
SP  - 161
EP  - 177
VL  - 21
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a15/
LA  - ru
ID  - TIMM_2015_21_4_a15
ER  - 
%0 Journal Article
%A N. A. Il'yasov
%T On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$
%J Trudy Instituta matematiki i mehaniki
%D 2015
%P 161-177
%V 21
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a15/
%G ru
%F TIMM_2015_21_4_a15
N. A. Il'yasov. On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 161-177. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a15/