{"paper":{"title":"Fractional Volterra-type operator induced by radial weight acting on Hardy space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"\\'Alvaro Miguel Moreno, Carlo Bellavita, Georgios Nikolaidis, Jos\\'e \\'Angel Pel\\'aez","submitted_at":"2025-06-22T18:09:43Z","abstract_excerpt":"Given a radial doubling weight $\\mu$ on the unit disc $\\mathbb{D}$ of the complex plane and its odd moments $\\mu_{2n+1}=\\int_0^1 s^{2n+1}\\mu(s)\\, ds$, we consider the fractional derivative\n  $$\n  D^\\mu(f)(z)=\\sum_{n=0}^{\\infty} \\frac{\\widehat{f}(n)}{\\mu_{2n+1}}z^n,\n  $$\n  of a function $ f(z)=\\sum_{n=0}^{\\infty}\\widehat{f}(n)z^n$ analytic in $\\mathbb{D}$. We also consider the fractional integral operator $I^\\mu(f)(z)=\\sum_{n=0}^{\\infty} \\mu_{2n+1}\\widehat{f}(n)z^n$, and the fractional Volterra-type operator\n  $$\n  V_{\\mu,g}(f)(z)= I^\\mu(f\\cdot D^\\mu(g))(z),\\quad f\\in\\mathcal{H}(\\mathbb{D}),\n  "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18122","kind":"arxiv","version":2},"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/2506.18122/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"}