{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LEMIYCB5HRR6IDXZ4AHDX3TQDP","short_pith_number":"pith:LEMIYCB5","schema_version":"1.0","canonical_sha256":"59188c083d3c63e40ef9e00e3bee701bce94d06568b9738356859b17fef0427e","source":{"kind":"arxiv","id":"1810.11331","version":1},"attestation_state":"computed","paper":{"title":"Weighted inequalities of Fefferman-Stein type for Riesz-Schr\\\"odinger Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bruno Bongioanni, Eleonor Harboure, Pablo Quijano","submitted_at":"2018-10-26T13:55:58Z","abstract_excerpt":"In this work we are concerned with Fefferman-Stein type inequalities. More precisely, given an operator $T$ and some $p$, $1<p<\\infty$, we look for operators $\\mathcal{M}$ such that the inequality $$\\int |Tf|^pw\\leq C\\int |f|^p \\mathcal{M}w$$ holds true for any weight $w$. Specifically, we are interested in the case of $T$ being any first or second order Riesz transform associated to the Schr\\\"odinger operator $L=-\\Delta + V$, with $V$ a non-negative function satisfying an appropriate reverse-H\\\"older condition. For the Riesz-Schr\\\"odinger transforms $\\nabla L^{-1/2}$ and $\\nabla^2 L^{-1}$ we "},"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":"1810.11331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-26T13:55:58Z","cross_cats_sorted":[],"title_canon_sha256":"10298dd9396bb89b7eec9c41a5e5be4ad6caf045e1c9a4833903224f0c8f3580","abstract_canon_sha256":"d23a4526844f19ca8672471b06b019779a794f18eee3b40881ad9e82bc74d447"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:14.462803Z","signature_b64":"mx5WOX0pJ1YfzEHyfQ1oaaMgiWJChWYwzr4I5H42yLmAYy3AmFnEQXjXMbnURXbuh1PqWg3So3TB+ftMdYoRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59188c083d3c63e40ef9e00e3bee701bce94d06568b9738356859b17fef0427e","last_reissued_at":"2026-05-18T00:02:14.462103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:14.462103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted inequalities of Fefferman-Stein type for Riesz-Schr\\\"odinger Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bruno Bongioanni, Eleonor Harboure, Pablo Quijano","submitted_at":"2018-10-26T13:55:58Z","abstract_excerpt":"In this work we are concerned with Fefferman-Stein type inequalities. More precisely, given an operator $T$ and some $p$, $1<p<\\infty$, we look for operators $\\mathcal{M}$ such that the inequality $$\\int |Tf|^pw\\leq C\\int |f|^p \\mathcal{M}w$$ holds true for any weight $w$. Specifically, we are interested in the case of $T$ being any first or second order Riesz transform associated to the Schr\\\"odinger operator $L=-\\Delta + V$, with $V$ a non-negative function satisfying an appropriate reverse-H\\\"older condition. For the Riesz-Schr\\\"odinger transforms $\\nabla L^{-1/2}$ and $\\nabla^2 L^{-1}$ we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11331","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":"1810.11331","created_at":"2026-05-18T00:02:14.462195+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.11331v1","created_at":"2026-05-18T00:02:14.462195+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11331","created_at":"2026-05-18T00:02:14.462195+00:00"},{"alias_kind":"pith_short_12","alias_value":"LEMIYCB5HRR6","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LEMIYCB5HRR6IDXZ","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LEMIYCB5","created_at":"2026-05-18T12:32:37.024351+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/LEMIYCB5HRR6IDXZ4AHDX3TQDP","json":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP.json","graph_json":"https://pith.science/api/pith-number/LEMIYCB5HRR6IDXZ4AHDX3TQDP/graph.json","events_json":"https://pith.science/api/pith-number/LEMIYCB5HRR6IDXZ4AHDX3TQDP/events.json","paper":"https://pith.science/paper/LEMIYCB5"},"agent_actions":{"view_html":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP","download_json":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP.json","view_paper":"https://pith.science/paper/LEMIYCB5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.11331&json=true","fetch_graph":"https://pith.science/api/pith-number/LEMIYCB5HRR6IDXZ4AHDX3TQDP/graph.json","fetch_events":"https://pith.science/api/pith-number/LEMIYCB5HRR6IDXZ4AHDX3TQDP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP/action/storage_attestation","attest_author":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP/action/author_attestation","sign_citation":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP/action/citation_signature","submit_replication":"https://pith.science/pith/LEMIYCB5HRR6IDXZ4AHDX3TQDP/action/replication_record"}},"created_at":"2026-05-18T00:02:14.462195+00:00","updated_at":"2026-05-18T00:02:14.462195+00:00"}