Wavelet and tent space characterizations of $h^p(\mathbb{R}^n)$, $0 < p \le 1$, with exact $L^2$ convergence, and the maximal class of admissible functions for Goldberg-type splittings

[2608.14960] Critical molecular theory and the maximal admissible class for Goldberg-type splittings of $h^p(\mathbb{R}^n)$, $0<p\le 1$ Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Classical Analysis and ODEs arXiv:2608.14960 (math) [Submitted on 15 Aug 2026 ( v1 ), last revised 9 Sep 2026 (this version, v4)] Title: Critical molecular theory and the maximal admissible class for Goldberg-type splittings of $h^p(\mathbb{R}^n)$, $0<p\le 1$ Authors: Mohamed El Aoumari View a PDF of the paper titled Critical molecular theory and the maximal admissible class for Goldberg-type splittings of $h^p(\mathbb{R}^n)$, $0<p\le 1$, by Mohamed El Aoumari View PDF HTML (experimental) Abstract: We identify the largest class of functions certifying membership in $h^p(\mathbb{R}^n)$, $0<p\le 1$, through Goldberg's convolution splitting: a critical Hölder modulus and an $\ell^p$-Dini decay majorant, sharp on the regularity, decay, and cancellation axes. The class reaches the critical decay $|x|^{-n/p}$, governed by a molecular theory extending the classical Taibleson-Weiss theory to every radius, with the resulting embedding shown sharp. Comments: 16 pages. v4: restores the $(p,q,η)$-molecule definition omitted from v3 and reorganizes the presentation, no result changed. The wavelet/tent space characterization and exact $L^2$ convergence of v1-v2 now form a separate submission, "Exact $L^2$ convergence through the wavelet and tent space characterizations of $h^p(\mathbb{R}^n)$, $0<p\le 1$" Subjects: Classical Analysis and ODEs (math.CA) ; Functional Analysis (math.FA) MSC classes: 42B30 (Primary) 42B35, 46E30, 46E15 (Secondary) Cite as: arXiv:2608.14960 [math.CA] (or arXiv:2608.14960v4 [math.CA] for this version) https://doi.org/10.48550/arXiv.2608.14960 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mohamed El Aoumari [ view email ] [v1] Sat, 15 Aug 2026 01:28:03 UTC (70 KB) [v2] Thu, 3 Sep 2026 21:41:02 UTC (68 KB) [v3] Mon, 7 Sep 2026 09:59:35 UTC (25 KB) [v4] Wed, 9 Sep 2026 19:00:05 UTC (26 KB) Full-text links: Access Paper: View a PDF of the paper titled Critical molecular theory and the maximal admissible class for Goldberg-type splittings of $h^p(\mathbb{R}^n)$, $0<p\le 1$, by Mohamed El Aoumari View PDF HTML (experimental) TeX Source view license Current browse context: math.CA < prev | next > new | recent | 2026-08 Change to browse by: math math.FA References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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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