{"paper":{"title":"Hardy-Sobolev type inequalities and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Bo-Yong Chen","submitted_at":"2017-12-06T05:32:00Z","abstract_excerpt":"This paper is devoted to various applications of Hardy-Sobolev type inequalities. We derive a new $L^2$ estimate for the $\\bar{\\partial}-$equation on ${\\mathbb C}^n$ which yields a quantitative generalization of the Hartogs extension theorem to the case when the singularity set is not necessary compact. We show that for any negative subharmonic function $\\psi$ on ${\\mathbb R}^n$, $n>2$, the BMO norm of $\\log |\\psi|$ is bounded above by $2\\sqrt{n-2}$ and $|\\psi|^\\gamma$ satisfies a reverse H\\\"older inequality for every $0<\\gamma<1$. We also show that every plurisubharmonic function is locally B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02044","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"}