{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GNPEPWN2RSZMK23FCXPGNUM76G","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":"ebcca5bf0e7703bcf9489333dedcbc52713706aaef9881445e8ecf73c55769d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-16T04:42:22Z","title_canon_sha256":"b023099121b97699394465b23b72d721bdc47395fd8de763ec47720cd4dcf5a7"},"schema_version":"1.0","source":{"id":"1503.04521","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04521","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04521v1","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04521","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"pith_short_12","alias_value":"GNPEPWN2RSZM","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GNPEPWN2RSZMK23F","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GNPEPWN2","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:cfe1a60bbe289e5f83983d245a0493c148dec47525dcadb23806478a618bf2f0","target":"graph","created_at":"2026-05-18T02:23:24Z","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":"In this paper we present a Calder\\'{o}n-Zygmund approach for a large class of parabolic equations with pseudo-differential operators $\\mathcal{A}(t)$ of arbitrary order $\\gamma\\in(0,\\infty)$. It is assumed that $\\cA(t)$ is merely measurable with respect to the time variable. The unique solvability of the equation $$ \\frac{\\partial u}{\\partial t}=\\cA u-\\lambda u+f, \\quad (t,x)\\in \\fR^{d+1} $$\n  and the $L_{q}(\\fR,L_{p})$-estimate $$ \\|u_{t}\\|_{L_{q}(\\fR,L_{p})}+\\|(-\\Delta)^{\\gamma/2}u\\|_{L_{q}(\\fR,L_{p})} +\\lambda\\|u\\|_{L_{q}(\\fR,L_{p})}\\leq N\\|f\\|_{L_{q}(\\fR,L_{p})} $$ are obtained for any $\\l","authors_text":"Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-16T04:42:22Z","title":"An $L_q(L_p)$-theory for parabolic pseudo-differential equations: Calder\\'on-Zygmund approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04521","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:a49d3ffeb3d821b27d431b4842384fe0fffeadd00f6825e3b505230f1c91af3e","target":"record","created_at":"2026-05-18T02:23:24Z","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":"ebcca5bf0e7703bcf9489333dedcbc52713706aaef9881445e8ecf73c55769d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-16T04:42:22Z","title_canon_sha256":"b023099121b97699394465b23b72d721bdc47395fd8de763ec47720cd4dcf5a7"},"schema_version":"1.0","source":{"id":"1503.04521","kind":"arxiv","version":1}},"canonical_sha256":"335e47d9ba8cb2c56b6515de66d19ff1a5b0ef69cecebc335610ad0c4399ed97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"335e47d9ba8cb2c56b6515de66d19ff1a5b0ef69cecebc335610ad0c4399ed97","first_computed_at":"2026-05-18T02:23:24.764249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:24.764249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lkFjoNN8RPttEz4OuxYY05MYwtOsBqZmIOW55W2eCbdiJjAy+/SKQPea9EoJmsHDu4VgOFniPV23AlsHBNplCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:24.764776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04521","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a49d3ffeb3d821b27d431b4842384fe0fffeadd00f6825e3b505230f1c91af3e","sha256:cfe1a60bbe289e5f83983d245a0493c148dec47525dcadb23806478a618bf2f0"],"state_sha256":"e2b82ccf74fa0670284a9c778cac240db3b7cca32f6aac12372ea9db56ede851"}