{"paper":{"title":"Coercivity of weighted Kohn Laplacians: the case of model monomial weights in $\\mathbb{C}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CV","authors_text":"Gian Maria Dall'Ara","submitted_at":"2015-02-09T18:49:03Z","abstract_excerpt":"The weighted Kohn Laplacian $\\Box_\\varphi$ is a natural second order elliptic operator associated to a weight $\\varphi:\\mathbb{C}^n\\rightarrow\\mathbb{R}$ and acting on $(0,1)$-forms, which plays a key role in several questions of complex analysis. We consider here the case of model monomial weights in $\\mathbb{C}^2$, i.e., $ \\varphi(z,w):=\\sum_{(\\alpha,\\beta)\\in\\Gamma}|z^\\alpha w^\\beta|^2, $ where $\\Gamma\\subseteq \\mathbb{N}^2$ is finite. Our goal is to prove coercivity estimates of the form $\\Box_\\varphi\\geq \\mu^2$, where $\\mu:\\mathbb{C}^n\\rightarrow\\mathbb{R}$ acts by pointwise multiplicatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02598","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"}