An Elementary Analog of the Operator Method in Additive Combinatorics
Matematičeskie zametki, Tome 109 (2021) no. 1, pp. 117-128
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper provides an elementary proof of inequalities previously obtained by the operator method and having applications in additive combinatorics. The method of proof allows us to take a new look at a certain special case of Sidorenko's conjecture.
Keywords: additive energy, operator method
Mots-clés : Sidorenko's conjecture.
@article{MZM_2021_109_1_a10,
     author = {K. I. Olmezov},
     title = {An {Elementary} {Analog} of the {Operator} {Method} in {Additive} {Combinatorics}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {117--128},
     year = {2021},
     volume = {109},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a10/}
}
TY  - JOUR
AU  - K. I. Olmezov
TI  - An Elementary Analog of the Operator Method in Additive Combinatorics
JO  - Matematičeskie zametki
PY  - 2021
SP  - 117
EP  - 128
VL  - 109
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a10/
LA  - ru
ID  - MZM_2021_109_1_a10
ER  - 
%0 Journal Article
%A K. I. Olmezov
%T An Elementary Analog of the Operator Method in Additive Combinatorics
%J Matematičeskie zametki
%D 2021
%P 117-128
%V 109
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a10/
%G ru
%F MZM_2021_109_1_a10
K. I. Olmezov. An Elementary Analog of the Operator Method in Additive Combinatorics. Matematičeskie zametki, Tome 109 (2021) no. 1, pp. 117-128. http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a10/

[1] I. D. Shkredov, “Some applications of W. Rudin's inequality to problems of combinatorial number theory”, Unif. Distrib. Theory, 6:2 (2011), 95–116 | MR | Zbl

[2] S. V. Konyagin, “Ob otsenke $L_1$-normy odnoi eksponentsialnoi summy”, Teoriya priblizhenii funktsii i operatorov, Tezisy dokladov Mezhdunarodnoi konferentsii, posvyaschennoi 80-letiyu so dnya rozhdeniya S. B. Stechkina, Ekaterinburg, 2000, 88–89

[3] T. Schoen, I. D. Shkredov, “On sumsets of convex sets”, Combin. Probab. Comput., 20:5 (2011), 793–798 | DOI | MR | Zbl

[4] T. Schoen, I. D. Shkredov, “Higher moments of convolutions”, J. Number Theory, 133:5 (2013), 1693–1737 | DOI | MR | Zbl

[5] I. D. Shkredov, “Neskolko novykh rezultatov o starshikh energiyakh”, Tr. MMO, 74, no. 1, MTsNMO, M., 2013, 35–73 | MR | Zbl

[6] K. I. Olmezov, A. S. Semchankau, I. D. Shkredov, On Popular Sums and Differences of Sets with Small Products, 2019, arXiv: 1911.12005v1

[7] I. D. Shkredov, “O summakh mnozhestv Semeredi–Trottera”, Izbrannye voprosy matematiki i mekhaniki, Tr. MIAN, 289, MAIK «Nauka/Interperiodika», M., 2015, 318–327 | DOI

[8] B. Murphy, M. Rudnev, I. D. Shkredov, Y. N. Shteinikov, On the Few Products, Many Sums Problem, 2017, arXiv: 1712.00410v1

[9] I. D. Shkredov, “Analiz Fure v kombinatornoi teorii chisel”, UMN, 65:3 (393) (2010), 127–184 | DOI | MR | Zbl

[10] A. Sidorenko, “A correlation inequality for bipartite graphs”, Graphs Combin., 9:2 (1993), 201–204 | DOI | MR | Zbl

[11] H. Hatami, “Graph norms and Sidorenko's conjecture”, Israel J. Math., 175 (2010), 125–150 | DOI | MR | Zbl

[12] D. Conlon, J. Fox, B. Sudakov, “An approximate version of Sidorenko's conjecture”, Geom. Funct. Anal., 20:6 (2010), 1354–1366 | DOI | MR | Zbl