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. 
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/
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