{"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"}