{"paper":{"title":"Area distortion under meromorphic mappings with nonzero pole having quasiconformal extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bappaditya Bhowmik, Goutam Satpati","submitted_at":"2017-11-23T13:26:32Z","abstract_excerpt":"Let $\\Sigma_k(p)$ be the class of univalent meromorphic functions defined on $\\mathbb{D}$ with $k$-quasiconformal extension to the extended complex plane $\\widehat{\\mathbb{C}}$, where $0\\leq k < 1$. Let $\\Sigma_k^0(p)$ be the class of functions $f \\in \\Sigma_k(p)$ having expansion of the form $f(z)= 1/(z-p) + \\sum_{n=1}^{\\infty}b_n z^{n}$ on $\\mathbb{D}$. In this article, we obtain sharp area distortion and weighted area distortion inequalities for functions in $\\Sigma_k^0(p)$. As a consequence of the obtained results, we present a sharp estimate for the bounds of the Hilbert transform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08684","kind":"arxiv","version":1},"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"}