{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:OSPHJULBS7RSTHYBT6TYAP6FL6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"49b697b9e15a6a99c1bf273add3027cd774e302c28e909523edcaa3b9c6c4dd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-05-21T21:13:14Z","title_canon_sha256":"6e160ddbcee2151f51b78ebff81bf9dca8946272ad705b222bfc6b7184496aaf"},"schema_version":"1.0","source":{"id":"2005.10909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.10909","created_at":"2026-07-05T01:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"2005.10909v1","created_at":"2026-07-05T01:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.10909","created_at":"2026-07-05T01:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"OSPHJULBS7RS","created_at":"2026-07-05T01:05:03Z"},{"alias_kind":"pith_short_16","alias_value":"OSPHJULBS7RSTHYB","created_at":"2026-07-05T01:05:03Z"},{"alias_kind":"pith_short_8","alias_value":"OSPHJULB","created_at":"2026-07-05T01:05:03Z"}],"graph_snapshots":[{"event_id":"sha256:5f9d454133ebb2a2591385e7c9498ece91c7ddca179e0f586552d27b8f76a69b","target":"graph","created_at":"2026-07-05T01:05:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2005.10909/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we characterize the boundedness, compactness, and weak compactness of the integration operators \\begin{align*} T_g (f)(z)=\\int_{0}^{z} f(w)g'(w)\\ dw \\end{align*} acting on the average radial integrability spaces $RM(p,q)$. For these purposes, we develop different tools such as a description of the bidual of $RM(p,0)$ and estimates of the norm of these spaces using the derivative of the functions, a family of results that we call Littlewood-Paley type inequalities.","authors_text":"Luis Rodr\\'iguez-Piazza, Manuel D. Contreras, Tanaus\\'u Aguilar-Hern\\'andez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-05-21T21:13:14Z","title":"Integration operators in average radial integrability spaces of analytic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.10909","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:08b44127da8be9bde147c7bcbe96f56569c6a5e88993534b0e62f4f127d86eea","target":"record","created_at":"2026-07-05T01:05:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"49b697b9e15a6a99c1bf273add3027cd774e302c28e909523edcaa3b9c6c4dd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-05-21T21:13:14Z","title_canon_sha256":"6e160ddbcee2151f51b78ebff81bf9dca8946272ad705b222bfc6b7184496aaf"},"schema_version":"1.0","source":{"id":"2005.10909","kind":"arxiv","version":1}},"canonical_sha256":"749e74d16197e3299f019fa7803fc55f83bdfd3eb0b8ac8288805caebc1dde8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"749e74d16197e3299f019fa7803fc55f83bdfd3eb0b8ac8288805caebc1dde8f","first_computed_at":"2026-07-05T01:05:03.518414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:05:03.518414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XTmHehQ/KvpPJNtlE/LjF8mw+hjXEahdUEsSDJNWlldz7LYcyVZ/2U28PYb/6XDltWxQwdFlw7nCJsu0lg6rBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:05:03.518867Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.10909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08b44127da8be9bde147c7bcbe96f56569c6a5e88993534b0e62f4f127d86eea","sha256:5f9d454133ebb2a2591385e7c9498ece91c7ddca179e0f586552d27b8f76a69b"],"state_sha256":"fc06723006187f4a336ea6308a84960cc738eddfb4ad4788c1a3b9b0835b8572"}