{"paper":{"title":"Exact regularity of the $\\bar{\\partial}$-problem with dependence on the $\\bar{\\partial}_b$-problem on weakly pseudoconvex domains in $\\mathbb{C}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Dariush Ehsani","submitted_at":"2014-06-28T10:24:19Z","abstract_excerpt":"We reduce the problem of constructing a linear solution operator to the $\\bar{\\partial}$-equation on smoothly bounded weakly pseudoconvex domains, $\\Omega$, in $\\mathbb{C}^2$ to the problem of the boundary $\\bar{\\partial}_b$-equation. We show there is a solution operator to $\\bar{\\partial}$ which is bounded as a map $W^{s}_{(0,1)}(\\Omega)\\cap{ker} \\bar{\\partial} \\rightarrow W^{s}(\\Omega)$ for all $s\\ge 0$ if there is a corresponding solution operator to the $\\bar{\\partial}_b$-problem with analogous regularity properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7381","kind":"arxiv","version":4},"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"}