{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IUCQ3TH6BGYCOJLWLJHENIMC5L","short_pith_number":"pith:IUCQ3TH6","schema_version":"1.0","canonical_sha256":"45050dccfe09b02725765a4e46a182eaca10fdcee47b255f71eae7458657d64a","source":{"kind":"arxiv","id":"1704.07997","version":1},"attestation_state":"computed","paper":{"title":"Carleson measures, BMO spaces and balayages associated to Schrodinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ji Li, Liang Song, Lixin Yan, Peng Chen, Xuan Thinh Duong","submitted_at":"2017-04-26T07:51:05Z","abstract_excerpt":"Let $\\L$ be a Schr\\\"odinger operator of the form $\\L=-\\Delta+V$ acting on $L^2(\\mathbb R^n)$, $n\\geq3$, where the nonnegative potential $V$ belongs to the reverse H\\\"older class $B_q$ for some $q\\geq n.$ Let ${\\rm BMO}_{{\\mathcal{L}}}(\\RR)$ denote the BMO space associated to the Schr\\\"odinger operator $\\L$ on $\\RR$. In this article we show that for every $f\\in {\\rm BMO}_{\\mathcal{L}}(\\RR)$ with compact support, then there exist $g\\in L^{\\infty}(\\RR)$ and a finite Carleson measure $\\mu$ such that $$\n  f(x)=g(x) + S_{\\mu, {\\mathcal P}}(x)\n  $$ with $\\|g\\|_{\\infty} +\\||\\mu\\||_{c}\\leq C \\|f\\|_{{\\r"},"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":"1704.07997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-26T07:51:05Z","cross_cats_sorted":[],"title_canon_sha256":"46b17bf4893ff308947fa451ca402d3661af232ca1dbb3450d6fa577cbc16c91","abstract_canon_sha256":"5422f58163f4744566eae3e9931d44d1cd62424e037be8941315d4b3d2c73121"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:31.302735Z","signature_b64":"//Y+Q4ruVdBebmZXmuYz7pLF++xI6gV3bKaJnkJu6yC2pBSixnsKUboGIGc3bZsX5Wgo0pgh3cpZyNEpDw0WDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45050dccfe09b02725765a4e46a182eaca10fdcee47b255f71eae7458657d64a","last_reissued_at":"2026-05-18T00:45:31.302111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:31.302111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Carleson measures, BMO spaces and balayages associated to Schrodinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ji Li, Liang Song, Lixin Yan, Peng Chen, Xuan Thinh Duong","submitted_at":"2017-04-26T07:51:05Z","abstract_excerpt":"Let $\\L$ be a Schr\\\"odinger operator of the form $\\L=-\\Delta+V$ acting on $L^2(\\mathbb R^n)$, $n\\geq3$, where the nonnegative potential $V$ belongs to the reverse H\\\"older class $B_q$ for some $q\\geq n.$ Let ${\\rm BMO}_{{\\mathcal{L}}}(\\RR)$ denote the BMO space associated to the Schr\\\"odinger operator $\\L$ on $\\RR$. In this article we show that for every $f\\in {\\rm BMO}_{\\mathcal{L}}(\\RR)$ with compact support, then there exist $g\\in L^{\\infty}(\\RR)$ and a finite Carleson measure $\\mu$ such that $$\n  f(x)=g(x) + S_{\\mu, {\\mathcal P}}(x)\n  $$ with $\\|g\\|_{\\infty} +\\||\\mu\\||_{c}\\leq C \\|f\\|_{{\\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07997","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":"1704.07997","created_at":"2026-05-18T00:45:31.302194+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.07997v1","created_at":"2026-05-18T00:45:31.302194+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07997","created_at":"2026-05-18T00:45:31.302194+00:00"},{"alias_kind":"pith_short_12","alias_value":"IUCQ3TH6BGYC","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IUCQ3TH6BGYCOJLW","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IUCQ3TH6","created_at":"2026-05-18T12:31:21.493067+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/IUCQ3TH6BGYCOJLWLJHENIMC5L","json":"https://pith.science/pith/IUCQ3TH6BGYCOJLWLJHENIMC5L.json","graph_json":"https://pith.science/api/pith-number/IUCQ3TH6BGYCOJLWLJHENIMC5L/graph.json","events_json":"https://pith.science/api/pith-number/IUCQ3TH6BGYCOJLWLJHENIMC5L/events.json","paper":"https://pith.science/paper/IUCQ3TH6"},"agent_actions":{"view_html":"https://pith.science/pith/IUCQ3TH6BGYCOJLWLJHENIMC5L","download_json":"https://pith.science/pith/IUCQ3TH6BGYCOJLWLJHENIMC5L.json","view_paper":"https://pith.science/paper/IUCQ3TH6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.07997&json=true","fetch_graph":"https://pith.science/api/pith-number/IUCQ3TH6BGYCOJLWLJHENIMC5L/graph.json","fetch_events":"https://pith.science/api/pith-number/IUCQ3TH6BGYCOJLWLJHENIMC5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IUCQ3TH6BGYCOJLWLJHENIMC5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IUCQ3TH6BGYCOJLWLJHENIMC5L/action/storage_attestation","attest_author":"https://pith.science/pith/IUCQ3TH6BGYCOJLWLJHENIMC5L/action/author_attestation","sign_citation":"https://pith.science/pith/IUCQ3TH6BGYCOJLWLJHENIMC5L/action/citation_signature","submit_replication":"https://pith.science/pith/IUCQ3TH6BGYCOJLWLJHENIMC5L/action/replication_record"}},"created_at":"2026-05-18T00:45:31.302194+00:00","updated_at":"2026-05-18T00:45:31.302194+00:00"}