Geodesic
On the Gowers Norms of Certain Functions
Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 609-627

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We consider functions $f(x,y)$ whose smallness condition for the rectangular norm implies the smallness of the rectangular norm for $f(x,x+y)$. We also study families of functions with a similar property for the higher Gowers norms. The method of proof is based on a transfer principle for sums between special systems of linear equations.
Keywords: Gowers norm, rectangular norm, probability measure, probability space, finite Abelian group, Parseval's inequality, Fourier series. 
@article{MZM_2012_92_4_a10,
     author = {I. D. Shkredov},
     title = {On the {Gowers} {Norms} of {Certain} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {609--627},
     publisher = {mathdoc},
     volume = {92},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a10/}
}
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I. D. Shkredov. On the Gowers Norms of Certain Functions. Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 609-627. http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a10/