{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:675M7WBVU6WNXORQ3GM7MUUM7W","short_pith_number":"pith:675M7WBV","schema_version":"1.0","canonical_sha256":"f7facfd835a7acdbba30d999f6528cfd9cc2c4cbb7d69a1bdf3710ca2e3dee80","source":{"kind":"arxiv","id":"1703.06200","version":1},"attestation_state":"computed","paper":{"title":"The effect of the smoothness of fractional type operators over their commutators with Lipschitz symbols on weighted spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Estefan\\'ia Dalmasso, Gladis Pradolini, Wilfredo Ramos","submitted_at":"2017-03-17T21:26:44Z","abstract_excerpt":"We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a H\\\"ormander's type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization resul"},"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":"1703.06200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-17T21:26:44Z","cross_cats_sorted":[],"title_canon_sha256":"e90c2d356254e9a86abd508b85d64a72ef28d0e98f4f5a5154f27aa6c80b717f","abstract_canon_sha256":"53198b76f194a57da75923edd1021a5628e278159351e7dc0c6995155d4a4d3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:11.428266Z","signature_b64":"qlLgCiwE5cagaXQZkIeFABp3oYUFYnBIuS5hrYP87zAZMwrgF6Q43IEzvFBgtRrkQJjeUxmKIqy4J5yUkJyIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7facfd835a7acdbba30d999f6528cfd9cc2c4cbb7d69a1bdf3710ca2e3dee80","last_reissued_at":"2026-05-18T00:12:11.427564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:11.427564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The effect of the smoothness of fractional type operators over their commutators with Lipschitz symbols on weighted spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Estefan\\'ia Dalmasso, Gladis Pradolini, Wilfredo Ramos","submitted_at":"2017-03-17T21:26:44Z","abstract_excerpt":"We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a H\\\"ormander's type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06200","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":"1703.06200","created_at":"2026-05-18T00:12:11.427674+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.06200v1","created_at":"2026-05-18T00:12:11.427674+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06200","created_at":"2026-05-18T00:12:11.427674+00:00"},{"alias_kind":"pith_short_12","alias_value":"675M7WBVU6WN","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"675M7WBVU6WNXORQ","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"675M7WBV","created_at":"2026-05-18T12:31:03.183658+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/675M7WBVU6WNXORQ3GM7MUUM7W","json":"https://pith.science/pith/675M7WBVU6WNXORQ3GM7MUUM7W.json","graph_json":"https://pith.science/api/pith-number/675M7WBVU6WNXORQ3GM7MUUM7W/graph.json","events_json":"https://pith.science/api/pith-number/675M7WBVU6WNXORQ3GM7MUUM7W/events.json","paper":"https://pith.science/paper/675M7WBV"},"agent_actions":{"view_html":"https://pith.science/pith/675M7WBVU6WNXORQ3GM7MUUM7W","download_json":"https://pith.science/pith/675M7WBVU6WNXORQ3GM7MUUM7W.json","view_paper":"https://pith.science/paper/675M7WBV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.06200&json=true","fetch_graph":"https://pith.science/api/pith-number/675M7WBVU6WNXORQ3GM7MUUM7W/graph.json","fetch_events":"https://pith.science/api/pith-number/675M7WBVU6WNXORQ3GM7MUUM7W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/675M7WBVU6WNXORQ3GM7MUUM7W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/675M7WBVU6WNXORQ3GM7MUUM7W/action/storage_attestation","attest_author":"https://pith.science/pith/675M7WBVU6WNXORQ3GM7MUUM7W/action/author_attestation","sign_citation":"https://pith.science/pith/675M7WBVU6WNXORQ3GM7MUUM7W/action/citation_signature","submit_replication":"https://pith.science/pith/675M7WBVU6WNXORQ3GM7MUUM7W/action/replication_record"}},"created_at":"2026-05-18T00:12:11.427674+00:00","updated_at":"2026-05-18T00:12:11.427674+00:00"}