{"paper":{"title":"Some new estimates for generalized fractional integrals associated with operators on Morrey spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hua Wang","submitted_at":"2026-05-19T05:11:42Z","abstract_excerpt":"Let $\\mathcal{L}$ be the infinitesimal generator of an analytic semigroup $\\big\\{e^{-t\\mathcal L}:t>0\\big\\}$ on $L^2(\\mathbb R^n)$ with Gaussian upper bounds, and suppose that $\\mathcal{L}$ has a bounded holomorphic functional calculus on $L^2(\\mathbb R^n)$. For given $0<\\alpha<n$, let $\\mathcal L^{-\\alpha/2}$ be the generalized fractional integral associated with $\\mathcal{L}$, which is given by \\begin{equation*} \\mathcal L^{-\\alpha/2}(f)(x):=\\frac{1}{\\Gamma(\\alpha/2)}\\int_0^{+\\infty}e^{-t\\mathcal L}(f)(x)t^{\\alpha/2-1}dt, \\end{equation*} where $\\Gamma(\\cdot)$ is the usual gamma function. In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19372","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/2605.19372/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"}