On Gowers norms of some functions

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.

15 pages

References in corpus (4)

• Hypergraph regularity and the multidimensional Szemerédi theorem
• An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm
• On polynomial approximations over $\mathbb{Z}/2^k\mathbb{Z}$
• Inverse Conjecture for the Gowers norm is false