Geodesic
On the Cantor–Lebesgue theorem for double trigonometric series
Matematičeskie zametki, Tome 12 (1972) no. 1, pp. 13-17 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Suppose that on some measurable set $E\subset\mathbf{T}^2$, $\mu(E)>2/3$, $$ A_\nu(x)=\sum_{n_1^2+n_2^2=\nu}c_{n_1,n_2}e^{2\pi i(n_1x_1+n_2x_2)}\to0\qquad(\nu\to\infty). $$ Then $$ \sum_{n_1^2+n_2^2=\nu}|c_{n_1,n_2}|^2\to0\qquad(\nu\to\infty). $$ 
@article{MZM_1972_12_1_a1,
     author = {S. B. Stechkin},
     title = {On the {Cantor{\textendash}Lebesgue} theorem for double trigonometric series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {13--17},
     year = {1972},
     volume = {12},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_1_a1/}
}
TY  - JOUR
AU  - S. B. Stechkin
TI  - On the Cantor–Lebesgue theorem for double trigonometric series
JO  - Matematičeskie zametki
PY  - 1972
SP  - 13
EP  - 17
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_1972_12_1_a1/
LA  - ru
ID  - MZM_1972_12_1_a1
ER  - 
%0 Journal Article
%A S. B. Stechkin
%T On the Cantor–Lebesgue theorem for double trigonometric series
%J Matematičeskie zametki
%D 1972
%P 13-17
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1972_12_1_a1/
%G ru
%F MZM_1972_12_1_a1
S. B. Stechkin. On the Cantor–Lebesgue theorem for double trigonometric series. Matematičeskie zametki, Tome 12 (1972) no. 1, pp. 13-17. http://geodesic.mathdoc.fr/item/MZM_1972_12_1_a1/