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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  "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.18122","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-06-22T18:09:43Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"d1827955daca9f1559443da8043ca04836d0a680d1d0643296f1ee9da600cd36","abstract_canon_sha256":"53bcbb41fef57ce4a352fd329dda855bf2288fb3bd847437e44def4544fc53c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:26:06.161929Z","signature_b64":"znrHba6aOG2IqYoDcufc36hx7/Gl+N4or90ATq30U8QbLQLo7b0Al9/j4JWCGODscfUOVi785POIvSJlJMXaDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fb5bc5bf11a4b36c578cf6e3b87a897c1d01dc38d4b1a4da4f903dfed92f674","last_reissued_at":"2026-07-05T11:26:06.161445Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:26:06.161445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.18122","created_at":"2026-07-05T11:26:06.161503+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.18122v2","created_at":"2026-07-05T11:26:06.161503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18122","created_at":"2026-07-05T11:26:06.161503+00:00"},{"alias_kind":"pith_short_12","alias_value":"J623YW7RDJFT","created_at":"2026-07-05T11:26:06.161503+00:00"},{"alias_kind":"pith_short_16","alias_value":"J623YW7RDJFTNRLY","created_at":"2026-07-05T11:26:06.161503+00:00"},{"alias_kind":"pith_short_8","alias_value":"J623YW7R","created_at":"2026-07-05T11:26:06.161503+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J623YW7RDJFTNRLYZ5XDXB5IS7","json":"https://pith.science/pith/J623YW7RDJFTNRLYZ5XDXB5IS7.json","graph_json":"https://pith.science/api/pith-number/J623YW7RDJFTNRLYZ5XDXB5IS7/graph.json","events_json":"https://pith.science/api/pith-number/J623YW7RDJFTNRLYZ5XDXB5IS7/events.json","paper":"https://pith.science/paper/J623YW7R"},"agent_actions":{"view_html":"https://pith.science/pith/J623YW7RDJFTNRLYZ5XDXB5IS7","download_json":"https://pith.science/pith/J623YW7RDJFTNRLYZ5XDXB5IS7.json","view_paper":"https://pith.science/paper/J623YW7R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.18122&json=true","fetch_graph":"https://pith.science/api/pith-number/J623YW7RDJFTNRLYZ5XDXB5IS7/graph.json","fetch_events":"https://pith.science/api/pith-number/J623YW7RDJFTNRLYZ5XDXB5IS7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J623YW7RDJFTNRLYZ5XDXB5IS7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J623YW7RDJFTNRLYZ5XDXB5IS7/action/storage_attestation","attest_author":"https://pith.science/pith/J623YW7RDJFTNRLYZ5XDXB5IS7/action/author_attestation","sign_citation":"https://pith.science/pith/J623YW7RDJFTNRLYZ5XDXB5IS7/action/citation_signature","submit_replication":"https://pith.science/pith/J623YW7RDJFTNRLYZ5XDXB5IS7/action/replication_record"}},"created_at":"2026-07-05T11:26:06.161503+00:00","updated_at":"2026-07-05T11:26:06.161503+00:00"}