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PreprintCC BY 4.0arXiv

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 → ℂ of degree at most m satisfies (∑|S|≤ m|f̂(S)|2m/(m+1))(m+1)/(2m) ≤ Km27|f|∞. The estimate is uniform in the dimension. The exponent $27$ is not optimized.

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Cite

BibTeXRIS
BibTeX
@misc{ivanisvili2026polynomial,
  title = {{Polynomial growth of Bohnenblust--Hille constants on the Hamming cube}},
  author = {Paata Ivanisvili},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12427},
  eprint = {2609.12427},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12427},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Polynomial growth of Bohnenblust--Hille constants on the Hamming cube
AU  - Paata Ivanisvili
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12427
UR  - https://arxiv.org/abs/2609.12427
AB  - 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 → ℂ of degree at most m satisfies (∑_|S|≤ m|f̂(S)|^2m/(m+1))^(m+1)/(2m) ≤ Km^27|f|_∞. The estimate is uniform in the dimension. The exponent $27$ is not optimized.
ER  -