{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LKB5AOHFI4VDMITZYUABWRTX2N","short_pith_number":"pith:LKB5AOHF","schema_version":"1.0","canonical_sha256":"5a83d038e5472a362279c5001b4677d34eb12f088f878dfde1b3c818217e01d2","source":{"kind":"arxiv","id":"1207.1293","version":1},"attestation_state":"computed","paper":{"title":"On improvement of summability properties in nonautonomous Kolmogorov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lorenzi, Luciana Angiuli","submitted_at":"2012-07-05T16:00:06Z","abstract_excerpt":"Under suitable conditions, we obtain some characterization of supercontractivity, ultraboundedness and ultracontractivity of the evolution operator $G(t,s)$ associated to a class of nonautonomous second order parabolic equations with unbounded coefficients defined in $I\\times\\R^d$, where $I$ is a right-halfline. For this purpose, we establish an Harnack type estimate for $G(t,s)$ and a family of logarithmic Sobolev inequalities with respect to the unique tight evolution system of measures $\\{\\mu_t: t \\in I\\}$ associated to $G(t,s)$. Sufficient conditions for the supercontractivity, ultrabounde"},"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":"1207.1293","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-05T16:00:06Z","cross_cats_sorted":[],"title_canon_sha256":"a9c072f259553e7c85e7e13d9631355256a88024fd73fec6ebb5e4bad042b48a","abstract_canon_sha256":"79480f54e57f860d9003d9f6d8cefe9bae59d0f131ffe80835bc59b4b892cc3b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:46.409287Z","signature_b64":"sDxEh72vTZTswyfq2lAm5bYC2h8ecDvnZ0wrRxLLqkZLLp+piPQOnnBDBel00AH/oro6dm0xEqI4jmpzRezyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a83d038e5472a362279c5001b4677d34eb12f088f878dfde1b3c818217e01d2","last_reissued_at":"2026-05-18T03:51:46.408446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:46.408446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On improvement of summability properties in nonautonomous Kolmogorov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lorenzi, Luciana Angiuli","submitted_at":"2012-07-05T16:00:06Z","abstract_excerpt":"Under suitable conditions, we obtain some characterization of supercontractivity, ultraboundedness and ultracontractivity of the evolution operator $G(t,s)$ associated to a class of nonautonomous second order parabolic equations with unbounded coefficients defined in $I\\times\\R^d$, where $I$ is a right-halfline. For this purpose, we establish an Harnack type estimate for $G(t,s)$ and a family of logarithmic Sobolev inequalities with respect to the unique tight evolution system of measures $\\{\\mu_t: t \\in I\\}$ associated to $G(t,s)$. Sufficient conditions for the supercontractivity, ultrabounde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1293","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":"1207.1293","created_at":"2026-05-18T03:51:46.408590+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.1293v1","created_at":"2026-05-18T03:51:46.408590+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1293","created_at":"2026-05-18T03:51:46.408590+00:00"},{"alias_kind":"pith_short_12","alias_value":"LKB5AOHFI4VD","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LKB5AOHFI4VDMITZ","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LKB5AOHF","created_at":"2026-05-18T12:27:14.488303+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/LKB5AOHFI4VDMITZYUABWRTX2N","json":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N.json","graph_json":"https://pith.science/api/pith-number/LKB5AOHFI4VDMITZYUABWRTX2N/graph.json","events_json":"https://pith.science/api/pith-number/LKB5AOHFI4VDMITZYUABWRTX2N/events.json","paper":"https://pith.science/paper/LKB5AOHF"},"agent_actions":{"view_html":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N","download_json":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N.json","view_paper":"https://pith.science/paper/LKB5AOHF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.1293&json=true","fetch_graph":"https://pith.science/api/pith-number/LKB5AOHFI4VDMITZYUABWRTX2N/graph.json","fetch_events":"https://pith.science/api/pith-number/LKB5AOHFI4VDMITZYUABWRTX2N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N/action/storage_attestation","attest_author":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N/action/author_attestation","sign_citation":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N/action/citation_signature","submit_replication":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N/action/replication_record"}},"created_at":"2026-05-18T03:51:46.408590+00:00","updated_at":"2026-05-18T03:51:46.408590+00:00"}