{"paper":{"title":"On the Green function and Poisson integrals of the Dunkl Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Margit R\\\"osler, Piotr Graczyk, Tomasz Luks","submitted_at":"2016-07-29T09:43:47Z","abstract_excerpt":"We prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian $\\Delta_k$ in $\\mathbb{R}^d$. As applications we derive the Poisson-Jensen formula for $\\Delta_k$-subharmonic functions and Hardy-Stein identities for the Poisson integrals of $\\Delta_k$. We also obtain sharp estimates of the Newton potential kernel, Green function and Poisson kernel in the rank one case in $\\mathbb{R}^d$. These estimates contrast sharply with the well-known results in the potential theory of the classical Laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08746","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"}