{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/regularity-estimates-of-fractional-heat","title":"Regularity estimates of fractional heat semigroups related with uniformly elliptic operators","arxiv_id":"2505.05333","date":"2025-05-08","proceeding":null,"authors":["Honglei Shi","Pengtao Li","Kai Zhao"],"abstract":"Let $L = -{\\rm div}( A(x) \\cdot \\nabla ) + V(x)$ be a second-order uniformly elliptic operator on $\\mathbb{ R }^{n}$ $(n\\geq 3)$, where $A(x)$ is a real symmetric matrix satisfying standard ellipticity conditions, and $V$ is a nonnegative potential belonging to the reverse H\\\"older class. For $ \\alpha \\in (0,1) $, we study regularity estimates of the fractional heat semigroups $ \\{ exp (-tL^ {\\alpha } )\\} _ { t > 0 }$, via the subordination formula and the fundamental solution of the associated uniformly parabolic equation $ \\partial_t u + Lu = 0 $. This approach avoids the use of Fourier transforms and is applicable to second-order differential operators whose heat kernels satisfy Gaussian upper bounds. As an application, we characterize the Campanato-type space $\\Lambda_{ L , \\gamma } \\left( \\mathbb{R}^n \\right)$ via the fractional heat semigroups $\\{exp ( - t L ^ {\\alpha } ) \\} _ { t > 0 } $.","url_abs":"https://arxiv.org/abs/2505.05333v1","url_pdf":"https://arxiv.org/pdf/2505.05333v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"regularity-estimates-of-fractional-heat","repo_url":"https://github.com/Shi-honglei/elliptic-operators-2025","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}