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We discuss estimates with loss of derivatives, in the sense of Kohn, for the system $(\\bar L_g,f^kL_g)$ where $(\\bar L_g,L_g)$ is $\\frac1{2m} $ subelliptic at 0 and $f(0)=0,\\,\\,df(0)\\neq0$. We prove estimates with a loss $l=\\frac{k-1}{2m} $ if the \"multiplier\" condition $|f|\\simgeq |g_{1\\bar 1}|^{\\frac1{2(m-1)}}$ is fulfilled. (For estimates without cut-off, subellipticity can be weakened to compactness and this results in a loss of $l=\\frac [{2(m-"},"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":"1208.5938","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-08-29T15:07:40Z","cross_cats_sorted":[],"title_canon_sha256":"80c7057e07bebbaff2b071d001dfa5a5a0898bc7d4da1c5c6491028d82c71f2f","abstract_canon_sha256":"f55be3859525473196ee8eaef42f69640ad08e955d04e12cd3f1772e39055dfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:54.273897Z","signature_b64":"iAVXdhgg+RGPGc7GZxhKAKjBD0PRsm+r/67POt9skBmRkZIhKiXB0lqvPsazZSGJ1WT3nifqlo9pplbDgTZvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8761837d61ac1999733481f77aa2431e5d2b27151336f2a80e6f23e470354104","last_reissued_at":"2026-05-18T02:49:54.273334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:54.273334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gain/Loss of derivatives for complex vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Giuseppe Zampieri, Luca Baracco","submitted_at":"2012-08-29T15:07:40Z","abstract_excerpt":"In $\\C_z\\times\\R_t$ we consider the function $g=g(z)$, set $g_1=\\di_z g$, $g_{1\\bar 1}=\\di_z\\dib_zg$ and define the operator $L_g=\\di_z+ig_1\\di_t$. We discuss estimates with loss of derivatives, in the sense of Kohn, for the system $(\\bar L_g,f^kL_g)$ where $(\\bar L_g,L_g)$ is $\\frac1{2m} $ subelliptic at 0 and $f(0)=0,\\,\\,df(0)\\neq0$. We prove estimates with a loss $l=\\frac{k-1}{2m} $ if the \"multiplier\" condition $|f|\\simgeq |g_{1\\bar 1}|^{\\frac1{2(m-1)}}$ is fulfilled. (For estimates without cut-off, subellipticity can be weakened to compactness and this results in a loss of $l=\\frac [{2(m-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5938","kind":"arxiv","version":2},"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":"1208.5938","created_at":"2026-05-18T02:49:54.273425+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.5938v2","created_at":"2026-05-18T02:49:54.273425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5938","created_at":"2026-05-18T02:49:54.273425+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q5QYG7LBVQMZ","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q5QYG7LBVQMZS4ZU","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q5QYG7LB","created_at":"2026-05-18T12:27:18.751474+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/Q5QYG7LBVQMZS4ZUQH3XVISDDZ","json":"https://pith.science/pith/Q5QYG7LBVQMZS4ZUQH3XVISDDZ.json","graph_json":"https://pith.science/api/pith-number/Q5QYG7LBVQMZS4ZUQH3XVISDDZ/graph.json","events_json":"https://pith.science/api/pith-number/Q5QYG7LBVQMZS4ZUQH3XVISDDZ/events.json","paper":"https://pith.science/paper/Q5QYG7LB"},"agent_actions":{"view_html":"https://pith.science/pith/Q5QYG7LBVQMZS4ZUQH3XVISDDZ","download_json":"https://pith.science/pith/Q5QYG7LBVQMZS4ZUQH3XVISDDZ.json","view_paper":"https://pith.science/paper/Q5QYG7LB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.5938&json=true","fetch_graph":"https://pith.science/api/pith-number/Q5QYG7LBVQMZS4ZUQH3XVISDDZ/graph.json","fetch_events":"https://pith.science/api/pith-number/Q5QYG7LBVQMZS4ZUQH3XVISDDZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q5QYG7LBVQMZS4ZUQH3XVISDDZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q5QYG7LBVQMZS4ZUQH3XVISDDZ/action/storage_attestation","attest_author":"https://pith.science/pith/Q5QYG7LBVQMZS4ZUQH3XVISDDZ/action/author_attestation","sign_citation":"https://pith.science/pith/Q5QYG7LBVQMZS4ZUQH3XVISDDZ/action/citation_signature","submit_replication":"https://pith.science/pith/Q5QYG7LBVQMZS4ZUQH3XVISDDZ/action/replication_record"}},"created_at":"2026-05-18T02:49:54.273425+00:00","updated_at":"2026-05-18T02:49:54.273425+00:00"}