Cotlar Properties, Hyperbolicity, and Unconditional Fourier Decompositions

[2408.10949] Cotlar Properties, Hyperbolicity, and Unconditional Fourier Decompositions Skip to main content Search Submit Donate Log in Mathematics > Functional Analysis arXiv:2408.10949 (math) [Submitted on 20 Aug 2024 ( v1 ), last revised 25 Aug 2026 (this version, v3)] Title: Cotlar Properties, Hyperbolicity, and Unconditional Fourier Decompositions Authors: Tao Mei View PDF HTML (experimental) Abstract: Let a discrete group $\Gamma$ act by isometries on a metric space $X$. We show that actions on geodesic hyperbolic spaces satisfy a branch Cotlar property. Under a finite low-orbit-frequency hypothesis, this yields uniform $L^4$-unconditionality for branch subspaces associated with sufficiently separated subsets; when the union of these branches has finite complement, the corresponding signed projections are uniformly bounded on $L^p(\widehat\Gamma)$ for every $1<p<\infty$. Finally, for connected vertex-transitive graphs, we prove that a scale-wise branch Cotlar property characterizes hyperbolicity of $X$. Comments: Added an equivalence result between the branch Cotlar property and the Hyperbolicity (Theorem 4.4) Subjects: Functional Analysis (math.FA) MSC classes: Primary 46L52, Secondary 43A15, 20F67 Cite as: arXiv:2408.10949 [math.FA] (or arXiv:2408.10949v3 [math.FA] for this version) https://doi.org/10.48550/arXiv.2408.10949 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Tao Mei [ view email ] [v1] Tue, 20 Aug 2024 15:41:36 UTC (10 KB) [v2] Wed, 12 Aug 2026 22:13:34 UTC (16 KB) [v3] Tue, 25 Aug 2026 02:16:59 UTC (21 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.FA < prev | next > new | recent | 2024-08 Change to browse by: math References & Citations NASA ADS 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

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