Author

Alexander Volberg

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Preprint Sep 2026

An $m^{2.943}$ Bohnenblust--Hille Bound on the Boolean Cube

Let $q_m=2m/(m+1)$ and put \[ \beta_0=\frac{3}{2}+\frac{1}{\log 2}=2.9426950408\ldots, \] where $\log$ is the natural logarithm. We give a proof scheme showing that, for every $\varepsilon>0$, there is $C_\varepsilon<\infty$ such that every complex-valued function $f:\{-1,1\}^n\to\C$ of Fourier degree at most $m$ satis...

Joseph Slote, Chun-Kai Tseng, Alexander Volberg · 1 citation · ⚡1

Preprint Sep 2026

Polynomial Bohnenblust--Hille bounds for product of cyclic groups

Fix an integer $K\ge2$, and let $C_K^n =\{(e^{\frac{2\pi ij}{K}})_{j=0}^{K-1}\}^n$ be the product of cyclic groups of order $K$. For a Fourier character $\chi_\alpha$, let $s(\alpha)$ be the number of active coordinates. We give a self-contained proposed proof that the dimension-free Bohnenblust--Hille constants govern...

Joseph Slote, Alexander Volberg · 3 citations · ⚡1