{"paper":{"title":"On properties of the solutions to the $\\alpha$-harmonic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Antti Rasila, Peijin Li, Zhi-Gang Wang","submitted_at":"2018-04-29T04:37:23Z","abstract_excerpt":"The aim of this paper is to establish properties of the solutions to the $\\alpha$-harmonic equations: $\\Delta_{\\alpha}(f(z))=\\partial{z}[(1-{|{z}|}^{2})^{-\\alpha} \\overline{\\partial}{z}f](z)=g(z)$, where $g:\\overline{\\mathbb{ID}}\\rightarrow\\mathbb{C}$ is a continuous function and $\\overline{\\mathbb{D}}$ denotes the closure of the unit disc $\\mathbb{D}$ in the complex plane $\\mathbb{C}$. We obtain Schwarz type and Schwarz-Pick type inequalities for the solutions to the $\\alpha$-harmonic equation. In particular, for $g\\equiv 0$, the solutions to the above equation are called $\\alpha$-harmonic fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10868","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"}