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Mathematical Notes

, Volume 92, Issue 3–4, pp 554–569 | Cite as

On the gowers norms of certain functions

  • I. D. ShkredovEmail author
Article
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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 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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