{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ZSAMFXLX4CYV7GR7TU4VGJUWLZ","short_pith_number":"pith:ZSAMFXLX","schema_version":"1.0","canonical_sha256":"cc80c2dd77e0b15f9a3f9d395326965e68b04368cd4773dd205b835bd0e4237a","source":{"kind":"arxiv","id":"1101.4329","version":1},"attestation_state":"computed","paper":{"title":"Weak compactness and essential norms of integration operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Jussi Laitila, Pekka J. Nieminen, Santeri Miihkinen","submitted_at":"2011-01-22T22:56:01Z","abstract_excerpt":"Let $g$ be an analytic function on the unit disc and consider the integration operator of the form $T_g f(z) = \\int_0^z fg'\\,d\\zeta$. We show that on the spaces $H^1$ and $BMOA$ the operator $T_g$ is weakly compact if and only if it is compact. In the case of $BMOA$ this answers a question of Siskakis and Zhao. More generally, we estimate the essential and weak essential norms of $T_g$ on $H^p$ and $BMOA$."},"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":"1101.4329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-01-22T22:56:01Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"a8b06efc52eb6beca7d45a655432e5377c21477d0687ebce58cd6d5e971e9ca6","abstract_canon_sha256":"bb5e52fa1a45ab53194ce6842d34025ce6082826a8f57d75de49a0dcbe934064"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:11.196171Z","signature_b64":"vcfXTl9AC9akOcZ9AAlCip6iWxwCj0vU/Z3WYK1qTsKTb87y2rpuFo+W9rv8YSopnkAdac23z4bGQX7jYCNHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc80c2dd77e0b15f9a3f9d395326965e68b04368cd4773dd205b835bd0e4237a","last_reissued_at":"2026-05-18T04:31:11.195667Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:11.195667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak compactness and essential norms of integration operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Jussi Laitila, Pekka J. Nieminen, Santeri Miihkinen","submitted_at":"2011-01-22T22:56:01Z","abstract_excerpt":"Let $g$ be an analytic function on the unit disc and consider the integration operator of the form $T_g f(z) = \\int_0^z fg'\\,d\\zeta$. We show that on the spaces $H^1$ and $BMOA$ the operator $T_g$ is weakly compact if and only if it is compact. In the case of $BMOA$ this answers a question of Siskakis and Zhao. More generally, we estimate the essential and weak essential norms of $T_g$ on $H^p$ and $BMOA$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4329","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":""},"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":"1101.4329","created_at":"2026-05-18T04:31:11.195753+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.4329v1","created_at":"2026-05-18T04:31:11.195753+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4329","created_at":"2026-05-18T04:31:11.195753+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZSAMFXLX4CYV","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZSAMFXLX4CYV7GR7","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZSAMFXLX","created_at":"2026-05-18T12:26:50.516681+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/ZSAMFXLX4CYV7GR7TU4VGJUWLZ","json":"https://pith.science/pith/ZSAMFXLX4CYV7GR7TU4VGJUWLZ.json","graph_json":"https://pith.science/api/pith-number/ZSAMFXLX4CYV7GR7TU4VGJUWLZ/graph.json","events_json":"https://pith.science/api/pith-number/ZSAMFXLX4CYV7GR7TU4VGJUWLZ/events.json","paper":"https://pith.science/paper/ZSAMFXLX"},"agent_actions":{"view_html":"https://pith.science/pith/ZSAMFXLX4CYV7GR7TU4VGJUWLZ","download_json":"https://pith.science/pith/ZSAMFXLX4CYV7GR7TU4VGJUWLZ.json","view_paper":"https://pith.science/paper/ZSAMFXLX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.4329&json=true","fetch_graph":"https://pith.science/api/pith-number/ZSAMFXLX4CYV7GR7TU4VGJUWLZ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZSAMFXLX4CYV7GR7TU4VGJUWLZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZSAMFXLX4CYV7GR7TU4VGJUWLZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZSAMFXLX4CYV7GR7TU4VGJUWLZ/action/storage_attestation","attest_author":"https://pith.science/pith/ZSAMFXLX4CYV7GR7TU4VGJUWLZ/action/author_attestation","sign_citation":"https://pith.science/pith/ZSAMFXLX4CYV7GR7TU4VGJUWLZ/action/citation_signature","submit_replication":"https://pith.science/pith/ZSAMFXLX4CYV7GR7TU4VGJUWLZ/action/replication_record"}},"created_at":"2026-05-18T04:31:11.195753+00:00","updated_at":"2026-05-18T04:31:11.195753+00:00"}