On Gowers norms of some functions
I.D. Shkredov

TL;DR
This paper investigates the relationship between Gowers norms of certain two-dimensional functions and their transformations, introducing methods based on transference principles for sums over linear systems.
Contribution
It establishes a connection between the smallness of Gowers norms of functions and their transformed versions, extending to higher norms and employing a novel transference approach.
Findings
Small Gowers norm of f(x,y) implies small norm of f(x,x+y)
Extended results for higher Gowers norms
Introduces a transference method for sums over linear systems
Abstract
We consider a class of two-dimensional functions f(x,y) with the property that the smallness of its rectangular norm implies the smallness of rectangular norm for f(x,x+y). Also we study a family of functions f(x,y) having a similar property for higher Gowers norms. The method based on a transference principle for a class of sums over special systems of linear equations.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Mathematical Dynamics and Fractals
