{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WLI6VT6IER6BYMLDWVVRZBAG3C","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":"2c0df9fa9048adf0688fb93807fde95514760a3c6e111f3f6709b23589be0752","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-06-17T18:35:25Z","title_canon_sha256":"049f48fcb693789b79e93082cd472ace37ef3e58f9c88761d776758dffcfb7ae"},"schema_version":"1.0","source":{"id":"1506.05414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05414","created_at":"2026-05-18T01:46:12Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05414v1","created_at":"2026-05-18T01:46:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05414","created_at":"2026-05-18T01:46:12Z"},{"alias_kind":"pith_short_12","alias_value":"WLI6VT6IER6B","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WLI6VT6IER6BYMLD","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WLI6VT6I","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:b628e5684b4128173de62dbeb20df66903de47ade48c25c96bd1f5375c1ee734","target":"graph","created_at":"2026-05-18T01:46:12Z","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"},"paper":{"abstract_excerpt":"We consider Volterra-type integration operators $T_g$ between Bergman spaces induced by weights $\\omega$ satisfying a doubling property. We derive estimates for the operator norms, essential and weak essential norms of $T_g: A_\\omega^p \\to A_\\omega^q$, $0<p\\leq q<\\infty$. In particular, the operator $T_g: A_\\omega^1\\to A_\\omega^1$ is weakly compact if and only if it is compact.","authors_text":"Pekka Nieminen, Santeri Miihkinen, Wen Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-06-17T18:35:25Z","title":"Essential norms and weak compactness of integral operators between weighted Bergman spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05414","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:e80bb74d2c76f79e5fabbafd8c6492c5765c146797c5d92813e2585dc4322580","target":"record","created_at":"2026-05-18T01:46:12Z","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":"2c0df9fa9048adf0688fb93807fde95514760a3c6e111f3f6709b23589be0752","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-06-17T18:35:25Z","title_canon_sha256":"049f48fcb693789b79e93082cd472ace37ef3e58f9c88761d776758dffcfb7ae"},"schema_version":"1.0","source":{"id":"1506.05414","kind":"arxiv","version":1}},"canonical_sha256":"b2d1eacfc8247c1c3163b56b1c8406d8801cf201f24ce9a4b838f89cb282d4c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2d1eacfc8247c1c3163b56b1c8406d8801cf201f24ce9a4b838f89cb282d4c5","first_computed_at":"2026-05-18T01:46:12.353891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:46:12.353891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O51GnkIFP++ddVOdorYyTi/HMlgyY9zxpVvcaSCLFUvuwZitSJbHCUI9ux/oNVXgmRPYbfI3yVuMMA7X1l0aCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:46:12.354467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.05414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e80bb74d2c76f79e5fabbafd8c6492c5765c146797c5d92813e2585dc4322580","sha256:b628e5684b4128173de62dbeb20df66903de47ade48c25c96bd1f5375c1ee734"],"state_sha256":"65072100b32e13b3ce7bba5bc08d87ae1e5c303a45e25769ce983cbf06e4c924"}