{"paper":{"title":"The raising steps method. Applications to the $\\bar \\partial $ equation in Stein manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Eric Amar (IMB)","submitted_at":"2013-12-30T08:24:34Z","abstract_excerpt":"In order to get estimates on the solutions of the equation $\\bar \\partial u=\\omega $ on Stein manifold, we introduce a new method the \"raising steps method\", to get global results from local ones. In particular it allows us to transfer results form open sets in ${\\mathbb{C}}^{n}$ to open sets in a Stein manifold.\\ \\par Using it we get $\\displaystyle L^{r}-L^{s}$ results for solutions of equation $\\bar \\partial u=\\omega $ with a gain, $\\displaystyle s>r,$ in strictly pseudo convex domains in Stein manifolds.\\ \\par We also get $\\displaystyle L^{r}-L^{s}$ results for domains in ${\\mathbb{C}}^{n}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7648","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"}