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Asymptotic Contractivity of Bohnenblust-Hille Constants with Bounded Monomial Support
Abstract
We study the optimal Bohnenblust-Hille constants $ K_{ m , M } $ for complex $ m $-homogeneous polynomials in any number of variables whose monomials with nonzero coefficient involve at most M variables. For every fixed M, we prove that these constants satisfy K m , M ≤ A M M / m · m ( M2 − 1 ) / ( 2m ) , for m ≥ M , where $ A_{ M } \geq 1 $ depends only on $ M $. In particular, K m , M → 1 as m → ∞ , and so the corresponding Bohnenblust-Hille constants are asymptotically contractive. The proof exploits the homogeneous structure through a decomposition according to exact monomial-support levels, partitions of the set of variables, multilinear Bohnenblust-Hille estimates, and interpolation with Parseval's identity.
Versions
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- Rigidity of Exact Contractivity in the Complex Polynomial Bohnenblust--Hille Inequality
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BibTeX
@misc{caromontoya2026asymptotic,
title = {{Asymptotic Contractivity of Bohnenblust-Hille Constants with Bounded Monomial Support}},
author = {Nicolás Caro-Montoya and Daniel Núñez-Alarcón and Diana Serrano-Rodríguez},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2607.20847},
eprint = {2607.20847},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.20847},
}
RIS
TY - UNPB
TI - Asymptotic Contractivity of Bohnenblust-Hille Constants with Bounded Monomial Support
AU - Nicolás Caro-Montoya
AU - Daniel Núñez-Alarcón
AU - Diana Serrano-Rodríguez
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2607.20847
UR - https://arxiv.org/abs/2607.20847
AB - We study the optimal Bohnenblust-Hille constants $ K_{ m , M } $ for complex $ m $-homogeneous polynomials in any number of variables whose monomials with nonzero coefficient involve at most M variables. For every fixed M, we prove that these constants satisfy K_ m , M ≤ A_ M ^ M / m · m^ ( M^2 − 1 ) / ( 2m ) , for m ≥ M , where $ A_{ M } \geq 1 $ depends only on $ M $. In particular, K_ m , M → 1 as m → ∞ , and so the corresponding Bohnenblust-Hille constants are asymptotically contractive. The proof exploits the homogeneous structure through a decomposition according to exact monomial-support levels, partitions of the set of variables, multilinear Bohnenblust-Hille estimates, and interpolation with Parseval's identity.
ER -