Geodesic
Discrete imbedding theorems and Lebesgue constants
Matematičeskie zametki, Tome 22 (1977) no. 3, pp. 381-394 
A. A. Yudin; V. A. Yudin. Discrete imbedding theorems and Lebesgue constants. Matematičeskie zametki, Tome 22 (1977) no. 3, pp. 381-394. http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a7/
@article{MZM_1977_22_3_a7,
     author = {A. A. Yudin and V. A. Yudin},
     title = {Discrete imbedding theorems and {Lebesgue} constants},
     journal = {Matemati\v{c}eskie zametki},
     pages = {381--394},
     year = {1977},
     volume = {22},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The order of growth of the Lebesgue constant for a “hyperbolic cross” is found: $$ L_R=\int_{T^2}\Bigl|\sum_{0<|\nu_1\nu_2|\le R_2}e^{2\pi i\nu x}\Bigr|\,dx\asymp R^{1.2},\quad R\to\infty. $$ Estimates are obtained by applying a discrete imbedding theorem. It is proved that among all convex domains in $E^2$, the square gives rise to a Lebesgue constant with the slowest growth $\ln^2R$.