{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:LW22GUCWLYW3KURFG4FEZSPVRY","short_pith_number":"pith:LW22GUCW","schema_version":"1.0","canonical_sha256":"5db5a350565e2db55225370a4cc9f58e13cfbf9948dac924d51789120b84adb1","source":{"kind":"arxiv","id":"1002.0792","version":2},"attestation_state":"computed","paper":{"title":"Second order elliptic operators with complex bounded measurable coefficients in $L^p$, Sobolev and Hardy spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alan McIntosh, Steve Hofmann, Svitlana Mayboroda","submitted_at":"2010-02-03T17:13:51Z","abstract_excerpt":"Let $L$ be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with $L$, such as the heat semigroup and Riesz transform, are not, in general, of Calder\\'on-Zygmund type and exhibit behavior different from their counterparts built upon the Laplacian. The current paper aims at a thorough description of the properties of such operators in $L^p$, Sobolev, and some new Hardy spaces naturally associated to $L$.\n  First, we show that the known ranges of boundedness in $L^p$ for the heat semigroup and Riesz transform of $L$"},"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":"1002.0792","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-02-03T17:13:51Z","cross_cats_sorted":[],"title_canon_sha256":"830f85efc1b8d730b01c14a428fc0487ab3490a660d0f1a6083ac4296dac631a","abstract_canon_sha256":"ca13bcd63a133edf14c0f6ba32bb2d5405f61004924b07a521e25f8415581933"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:55.340410Z","signature_b64":"7/ZeCaeDhzqhBPavm/V/Q5ciNmxvJZlm9gWCrTsh3+8YE74BgdyyE6/x0UZ+Hmf6gIYoPxiSzSVZMkm8O8TQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5db5a350565e2db55225370a4cc9f58e13cfbf9948dac924d51789120b84adb1","last_reissued_at":"2026-05-18T04:34:55.339632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:55.339632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second order elliptic operators with complex bounded measurable coefficients in $L^p$, Sobolev and Hardy spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alan McIntosh, Steve Hofmann, Svitlana Mayboroda","submitted_at":"2010-02-03T17:13:51Z","abstract_excerpt":"Let $L$ be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with $L$, such as the heat semigroup and Riesz transform, are not, in general, of Calder\\'on-Zygmund type and exhibit behavior different from their counterparts built upon the Laplacian. The current paper aims at a thorough description of the properties of such operators in $L^p$, Sobolev, and some new Hardy spaces naturally associated to $L$.\n  First, we show that the known ranges of boundedness in $L^p$ for the heat semigroup and Riesz transform of $L$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0792","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":""},"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":"1002.0792","created_at":"2026-05-18T04:34:55.339738+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.0792v2","created_at":"2026-05-18T04:34:55.339738+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0792","created_at":"2026-05-18T04:34:55.339738+00:00"},{"alias_kind":"pith_short_12","alias_value":"LW22GUCWLYW3","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"LW22GUCWLYW3KURF","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"LW22GUCW","created_at":"2026-05-18T12:26:10.704358+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/LW22GUCWLYW3KURFG4FEZSPVRY","json":"https://pith.science/pith/LW22GUCWLYW3KURFG4FEZSPVRY.json","graph_json":"https://pith.science/api/pith-number/LW22GUCWLYW3KURFG4FEZSPVRY/graph.json","events_json":"https://pith.science/api/pith-number/LW22GUCWLYW3KURFG4FEZSPVRY/events.json","paper":"https://pith.science/paper/LW22GUCW"},"agent_actions":{"view_html":"https://pith.science/pith/LW22GUCWLYW3KURFG4FEZSPVRY","download_json":"https://pith.science/pith/LW22GUCWLYW3KURFG4FEZSPVRY.json","view_paper":"https://pith.science/paper/LW22GUCW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.0792&json=true","fetch_graph":"https://pith.science/api/pith-number/LW22GUCWLYW3KURFG4FEZSPVRY/graph.json","fetch_events":"https://pith.science/api/pith-number/LW22GUCWLYW3KURFG4FEZSPVRY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LW22GUCWLYW3KURFG4FEZSPVRY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LW22GUCWLYW3KURFG4FEZSPVRY/action/storage_attestation","attest_author":"https://pith.science/pith/LW22GUCWLYW3KURFG4FEZSPVRY/action/author_attestation","sign_citation":"https://pith.science/pith/LW22GUCWLYW3KURFG4FEZSPVRY/action/citation_signature","submit_replication":"https://pith.science/pith/LW22GUCWLYW3KURFG4FEZSPVRY/action/replication_record"}},"created_at":"2026-05-18T04:34:55.339738+00:00","updated_at":"2026-05-18T04:34:55.339738+00:00"}