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Mat. Zametki, 2012, Volume 92, Issue 4, Pages 609–627 (Mi mz8934)  

On the Gowers Norms of Certain Functions

I. D. Shkredov

M. V. Lomonosov Moscow State University

Abstract: 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

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00759
Ministry of Education and Science of the Russian Federation НШ-8684.2010.1


DOI: https://doi.org/10.4213/mzm8934

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English version:
Mathematical Notes, 2012, 92:4, 554–569

Bibliographic databases:

Document Type: Article
UDC: 519.237.4
Received: 26.09.2010
Revised: 19.05.2011

Citation: I. D. Shkredov, “On the Gowers Norms of Certain Functions”, Mat. Zametki, 92:4 (2012), 609–627; Math. Notes, 92:4 (2012), 554–569

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