Sharp estimates for Gowers norms on discrete cubes

Adrian Beker, Tonći Crmarić, Vjekoslav Kovač

We study optimal dimensionless inequalities $$\Vert f{\Vert }_{U^k}\le \Vert f{\Vert }_{{\ell }^{p_{k,n}}}$$ that hold for all functions $f:{\mathbb{Z}}^d\to \mathbb{C}$ supported in $\{0,1,\ldots,…