{"paper":{"title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Estefan\\'ia Dalmasso, Jorge J. Betancor, Pablo Quijano","submitted_at":"2025-06-17T15:26:04Z","abstract_excerpt":"In this paper we consider fractional Kolmogorov operators defined, in $\\mathbb{R}^d$, by\n  \\[\\Lambda_\\kappa=(-\\Delta)^{\\alpha/2}+\\frac{\\kappa}{|x|^\\alpha} x\\cdot \\nabla,\\]\n  with $\\alpha\\in (1,2)$, $\\alpha<(d+2)/2$ and $\\kappa\\in \\mathbb{R}$. The operator $\\Lambda_\\alpha$ generates a holomorphic semigroup $\\{T_t^\\alpha\\}_{t>0}$ in $L^2(\\mathbb{R}^d)$ provided that $\\kappa<\\kappa_c$ where $\\kappa_c$ is a critical coupling constant. We establish $L^p$-boundedness properties for the variation operators $V_\\rho\\left(\\{t^\\ell\\partial_t^\\ell T_t^\\alpha\\}_{t>0}\\right)$ with $\\rho> 2$, $\\ell\\in \\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.14631","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.14631/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}