Asymptotic Contractivity of Bohnenblust-Hille Constants with Bounded Monomial Support

[2607.20847] Asymptotic Contractivity of Bohnenblust-Hille Constants with Bounded Monomial Support Skip to main content Search Submit Donate Log in Mathematics > Functional Analysis arXiv:2607.20847 (math) [Submitted on 23 Jul 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Asymptotic Contractivity of Bohnenblust-Hille Constants with Bounded Monomial Support Authors: Nicolás Caro-Montoya , Daniel Núñez-Alarcón , Diana Serrano-Rodríguez View PDF HTML (experimental) 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 \[ K_{ m , M } \leq A_{ M }^{ M / m } \cdot m^{ ( M^2 - 1 ) / ( 2m ) } \, , \quad \text{for} \ m \geq M \, , \] where $ A_{ M } \geq 1 $ depends only on $ M $. In particular, \[ K_{ m , M } \to 1 \quad \text{as} \ m \to \infty \, , \] 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. Comments: Expanded and revised. To appear in Bulletin of the Brazilian Mathematical Society Subjects: Functional Analysis (math.FA) MSC classes: 46G25, 32A05 Cite as: arXiv:2607.20847 [math.FA] (or arXiv:2607.20847v2 [math.FA] for this version) https://doi.org/10.48550/arXiv.2607.20847 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1007/s00574-026-00527-1 Focus to learn more DOI(s) linking to related resources Submission history From: Daniel Núñez Alarcón Professor [ view email ] [v1] Thu, 23 Jul 2026 02:19:14 UTC (8 KB) [v2] Fri, 28 Aug 2026 02:19:10 UTC (13 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.FA < prev | next > new | recent | 2026-07 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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