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PreprintarXiv licencearXiv

The Geometry of Real Anisotropic Bohnenblust--Hille Constants

  • Daniel Nunez-Alarcon
  • Daniel M. Pellegrino
  • Joedson Silva dos Santos
  • Diana Marcela Serrano-Rodriguez
  • Eduardo V. Teixeira
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Abstract

We determine the growth scale of the optimal constants in the real anisotropic Bohnenblust--Hille inequality. For an exponent vector q(m), write Cq(m)(m) for its optimal constant and dm for its diameter. These constants are superpolynomial precisely when m dm/log m→∞; throughout this regime, their logarithm has the sharp scale m dm. If also dm→0, then log Cq(m)(m)/(m dm) lies asymptotically in the interval [(log 2)/4,(2−log 2−γ)/4], where γ is the Euler--Mascheroni constant; this interval has width less than 10−2. We also solve the extremal problems at fixed diameter and fixed total deficit. The normalized reciprocal-deficit profiles order the canonically arranged optimal constants by majorization, yield exact formulas on a full-dimensional region, and recover the lower coefficient (log 2)/4 throughout a broad class of anisotropic regimes.

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Cite

BibTeXRIS
BibTeX
@misc{nunezalarcon2026geometry,
  title = {{The Geometry of Real Anisotropic Bohnenblust--Hille Constants}},
  author = {Daniel Nunez-Alarcon and Daniel M. Pellegrino and Joedson Silva dos Santos and Diana Marcela Serrano-Rodriguez and Eduardo V. Teixeira},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04143},
  eprint = {2609.04143},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04143},
}
RIS
TY  - UNPB
TI  - The Geometry of Real Anisotropic Bohnenblust--Hille Constants
AU  - Daniel Nunez-Alarcon
AU  - Daniel M. Pellegrino
AU  - Joedson Silva dos Santos
AU  - Diana Marcela Serrano-Rodriguez
AU  - Eduardo V. Teixeira
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04143
UR  - https://arxiv.org/abs/2609.04143
AB  - We determine the growth scale of the optimal constants in the real anisotropic Bohnenblust--Hille inequality. For an exponent vector q^(m), write C_q^(m)^(m) for its optimal constant and d_m for its diameter. These constants are superpolynomial precisely when m d_m/log m→∞; throughout this regime, their logarithm has the sharp scale m d_m. If also d_m→0, then log C_q^(m)^(m)/(m d_m) lies asymptotically in the interval [(log 2)/4,(2−log 2−γ)/4], where γ is the Euler--Mascheroni constant; this interval has width less than 10^−2. We also solve the extremal problems at fixed diameter and fixed total deficit. The normalized reciprocal-deficit profiles order the canonically arranged optimal constants by majorization, yield exact formulas on a full-dimensional region, and recover the lower coefficient (log 2)/4 throughout a broad class of anisotropic regimes.
ER  -