{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3SVWEMHPPYSIL44OK2EZT6J5ID","short_pith_number":"pith:3SVWEMHP","schema_version":"1.0","canonical_sha256":"dcab6230ef7e2485f38e568999f93d40de7c30e19a234455290b6c1d132e03ab","source":{"kind":"arxiv","id":"1803.10652","version":1},"attestation_state":"computed","paper":{"title":"$p$-regularity and weights for operators between $L^p$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Enrique A. S\\'anchez P\\'erez, Pedro Tradacete","submitted_at":"2018-03-28T14:39:49Z","abstract_excerpt":"We explore the connection between $p$-regular operators on Banach function spaces and weighted $p$-estimates. In particular, our results focus on the following problem. Given finite measure spaces $\\mu$ and $\\nu$, let $T$ be an operator defined from a Banach function space $X(\\nu)$ and taking values on $L^p (v d \\mu)$ for $v$ in certain family of weights $V\\subset L^1(\\mu)_+$: we analyze the existence of a bounded family of weights $W\\subset L^1(\\nu)_+$ such that for every $v\\in V$ there is $w \\in W$ in such a way that $T:L^p(w d \\nu) \\to L^p(v d \\mu)$ is continuous uniformly on $V$. A conditi"},"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":"1803.10652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-28T14:39:49Z","cross_cats_sorted":[],"title_canon_sha256":"3ae46d5e12dab97068dff9e31ccdce34e437ff795432075456c467142f0e2c30","abstract_canon_sha256":"3b54762cdd1eab1869620458c0da809734eae42163b28dd2c16150cb04f7c67e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:54.559934Z","signature_b64":"HfELQcIX3fWwyMzCEcTd3Qj2w4gIgmLWz5brAqKQa1esp3KqnSOr6WOBGW6yshlv4Z7sAsNhnWNNo6BlPJePAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcab6230ef7e2485f38e568999f93d40de7c30e19a234455290b6c1d132e03ab","last_reissued_at":"2026-05-18T00:19:54.559209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:54.559209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$p$-regularity and weights for operators between $L^p$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Enrique A. S\\'anchez P\\'erez, Pedro Tradacete","submitted_at":"2018-03-28T14:39:49Z","abstract_excerpt":"We explore the connection between $p$-regular operators on Banach function spaces and weighted $p$-estimates. In particular, our results focus on the following problem. Given finite measure spaces $\\mu$ and $\\nu$, let $T$ be an operator defined from a Banach function space $X(\\nu)$ and taking values on $L^p (v d \\mu)$ for $v$ in certain family of weights $V\\subset L^1(\\mu)_+$: we analyze the existence of a bounded family of weights $W\\subset L^1(\\nu)_+$ such that for every $v\\in V$ there is $w \\in W$ in such a way that $T:L^p(w d \\nu) \\to L^p(v d \\mu)$ is continuous uniformly on $V$. A conditi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10652","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":"1803.10652","created_at":"2026-05-18T00:19:54.559331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.10652v1","created_at":"2026-05-18T00:19:54.559331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10652","created_at":"2026-05-18T00:19:54.559331+00:00"},{"alias_kind":"pith_short_12","alias_value":"3SVWEMHPPYSI","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"3SVWEMHPPYSIL44O","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"3SVWEMHP","created_at":"2026-05-18T12:32:05.422762+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/3SVWEMHPPYSIL44OK2EZT6J5ID","json":"https://pith.science/pith/3SVWEMHPPYSIL44OK2EZT6J5ID.json","graph_json":"https://pith.science/api/pith-number/3SVWEMHPPYSIL44OK2EZT6J5ID/graph.json","events_json":"https://pith.science/api/pith-number/3SVWEMHPPYSIL44OK2EZT6J5ID/events.json","paper":"https://pith.science/paper/3SVWEMHP"},"agent_actions":{"view_html":"https://pith.science/pith/3SVWEMHPPYSIL44OK2EZT6J5ID","download_json":"https://pith.science/pith/3SVWEMHPPYSIL44OK2EZT6J5ID.json","view_paper":"https://pith.science/paper/3SVWEMHP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.10652&json=true","fetch_graph":"https://pith.science/api/pith-number/3SVWEMHPPYSIL44OK2EZT6J5ID/graph.json","fetch_events":"https://pith.science/api/pith-number/3SVWEMHPPYSIL44OK2EZT6J5ID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3SVWEMHPPYSIL44OK2EZT6J5ID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3SVWEMHPPYSIL44OK2EZT6J5ID/action/storage_attestation","attest_author":"https://pith.science/pith/3SVWEMHPPYSIL44OK2EZT6J5ID/action/author_attestation","sign_citation":"https://pith.science/pith/3SVWEMHPPYSIL44OK2EZT6J5ID/action/citation_signature","submit_replication":"https://pith.science/pith/3SVWEMHPPYSIL44OK2EZT6J5ID/action/replication_record"}},"created_at":"2026-05-18T00:19:54.559331+00:00","updated_at":"2026-05-18T00:19:54.559331+00:00"}