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This operator generalizes the classical Ces\\`aro operator (corresponding to the case where $\\mu$ is the Lebe"},"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":"2507.20586","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-07-28T07:45:19Z","cross_cats_sorted":[],"title_canon_sha256":"7c7cff21aa1c15a1eaddd845c9a9f07b4b19a20d2770cc40528c38e239844b0e","abstract_canon_sha256":"aaeffcd906353697afbce61778317f1cd95b0be1a6adebd9a202498a356934a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:44:22.107330Z","signature_b64":"oNGk+Db1OfexcdQvb6GEoLCxcvnIiqmfzBORcodJYnbhCMdJxVUU5A90ychwQhTjVN7xO37036QNM8VF/a3WDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"151ff9915c654d9ceea21905c9dc8ac603954ab113aaae7f14d3a3d0132e137a","last_reissued_at":"2026-07-05T11:44:22.106920Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:44:22.106920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ces\\`aro-type operators on mixed norm spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alejandro Mas, \\'Oscar Blasco","submitted_at":"2025-07-28T07:45:19Z","abstract_excerpt":"Given a positive Borel measure $\\mu$ on $[0,1)$ and a parameter $\\beta>0$, we consider the Ces\\`aro-type operator $\\mathcal C_{\\mu,\\beta}$ acting on the analytic function $f(z)=\\sum_{n=0}^\\infty a_n z^n$ on the unit disc of the complex plane $\\mathbb D$, defined by \\[ \\mathcal C_{\\mu,\\beta}(f)(z)= \\sum_{n=0}^\\infty \\mu_n \\left( \\sum_{k=0}^n \\frac{\\Gamma(n-k+\\beta)}{(n-k)! \\Gamma(\\beta)} a_k \\right) z^n = \\int_0^1 \\frac{f(tz)}{(1-tz)^\\beta} d\\mu(t), \\] where $\\mu_n=\\int_0^1 t^n d\\mu(t)$. This operator generalizes the classical Ces\\`aro operator (corresponding to the case where $\\mu$ is the Lebe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20586","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/2507.20586/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":"2507.20586","created_at":"2026-07-05T11:44:22.106977+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.20586v1","created_at":"2026-07-05T11:44:22.106977+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20586","created_at":"2026-07-05T11:44:22.106977+00:00"},{"alias_kind":"pith_short_12","alias_value":"CUP7TEK4MVGZ","created_at":"2026-07-05T11:44:22.106977+00:00"},{"alias_kind":"pith_short_16","alias_value":"CUP7TEK4MVGZZ3VC","created_at":"2026-07-05T11:44:22.106977+00:00"},{"alias_kind":"pith_short_8","alias_value":"CUP7TEK4","created_at":"2026-07-05T11:44:22.106977+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/CUP7TEK4MVGZZ3VCDEC4TXEKYY","json":"https://pith.science/pith/CUP7TEK4MVGZZ3VCDEC4TXEKYY.json","graph_json":"https://pith.science/api/pith-number/CUP7TEK4MVGZZ3VCDEC4TXEKYY/graph.json","events_json":"https://pith.science/api/pith-number/CUP7TEK4MVGZZ3VCDEC4TXEKYY/events.json","paper":"https://pith.science/paper/CUP7TEK4"},"agent_actions":{"view_html":"https://pith.science/pith/CUP7TEK4MVGZZ3VCDEC4TXEKYY","download_json":"https://pith.science/pith/CUP7TEK4MVGZZ3VCDEC4TXEKYY.json","view_paper":"https://pith.science/paper/CUP7TEK4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.20586&json=true","fetch_graph":"https://pith.science/api/pith-number/CUP7TEK4MVGZZ3VCDEC4TXEKYY/graph.json","fetch_events":"https://pith.science/api/pith-number/CUP7TEK4MVGZZ3VCDEC4TXEKYY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CUP7TEK4MVGZZ3VCDEC4TXEKYY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CUP7TEK4MVGZZ3VCDEC4TXEKYY/action/storage_attestation","attest_author":"https://pith.science/pith/CUP7TEK4MVGZZ3VCDEC4TXEKYY/action/author_attestation","sign_citation":"https://pith.science/pith/CUP7TEK4MVGZZ3VCDEC4TXEKYY/action/citation_signature","submit_replication":"https://pith.science/pith/CUP7TEK4MVGZZ3VCDEC4TXEKYY/action/replication_record"}},"created_at":"2026-07-05T11:44:22.106977+00:00","updated_at":"2026-07-05T11:44:22.106977+00:00"}