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arXiv · 2609.12427

Polynomial growth of Bohnenblust--Hille constants on the Hamming cube

Paata Ivanisvili
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Abstract

We prove that the Bohnenblust--Hille constants for Walsh polynomials on the Hamming cube grow at most polynomially in the degree. More precisely, there is an absolute constant $K$ such that every $f :\{-1,1\}^{n} \to \mathbb{C}$ of degree at most $m$ satisfies $$ \left(\sum_{|S|\le m}|\widehat f(S)|^{2m/(m+1)}\right)^{(m+1)/(2m)} \le Km^{27}\|f\|_\infty. $$ The estimate is uniform in the dimension. The exponent $27$ is not optimized.

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Paata Ivanisvili. 2026-09-11. Polynomial growth of Bohnenblust--Hille constants on the Hamming cube. https://arxiv.org/abs/2609.12427

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