[2401.04504] A unified approach to $L^p$ Hardy and Rellich-type inequalities in Euclidean and non-Euclidean settings Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2401.04504 (math) [Submitted on 9 Jan 2024 ( v1 ), last revised 17 Nov 2025 (this version, v2)] Title: A unified approach to $L^p$ Hardy and Rellich-type inequalities in Euclidean and non-Euclidean settings Authors: Lorenzo D'Arca View a PDF of the paper titled A unified approach to $L^p$ Hardy and Rellich-type inequalities in Euclidean and non-Euclidean settings, by Lorenzo D'Arca View PDF HTML (experimental) Abstract: We present a unified and concise method for establishing L^p Hardy and Rellich inequalities for a broad class of subelliptic operators of divergence type. The approach, based on a fundamental algebraic identity, provides explicit control on maximizing sequences and yields sharp constants in several significant cases. It applies beyond the Euclidean framework, covering the Heisenberg and Carnot group settings, and extends to a variety of subelliptic operators such as the Heisenberg-Greiner and Baouendi-Grushin operators. Comments: This version incorporates a substantial revision of the manuscript. The exposition has been streamlined, several sections have been reorganized or removed, and the overall structure has been improved Subjects: Analysis of PDEs (math.AP) ; Spectral Theory (math.SP) MSC classes: 26D10 (Primary) 35A23, 35R03 (Secondary) Cite as: arXiv:2401.04504 [math.AP] (or arXiv:2401.04504v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2401.04504 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Journal of Inequalities and Applications 2026, 38 (2026) Related DOI : https://doi.org/10.1186/s13660-026-03449-0 Focus to learn more DOI(s) linking to related resources Submission history From: Lorenzo D'Arca [ view email ] [v1] Tue, 9 Jan 2024 11:47:38 UTC (26 KB) [v2] Mon, 17 Nov 2025 17:46:43 UTC (21 KB) Full-text links: Access Paper: View a PDF of the paper titled A unified approach to $L^p$ Hardy and Rellich-type inequalities in Euclidean and non-Euclidean settings, by Lorenzo D'Arca View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2024-01 Change to browse by: math math.SP 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