{"paper":{"title":"Harmonic functions, conjugate harmonic functions and the Hardy space $H^1$ in the rational Dunkl setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Agnieszka Hejna, Jacek Dziuba\\'nski, Jean-Philippe Anker","submitted_at":"2018-02-19T12:25:05Z","abstract_excerpt":"In this work we extend the theory of the classical Hardy space $H^1$ to the rational Dunkl setting. Specifically, let $\\Delta$ be the Dunkl Laplacian on a Euclidean space $\\mathbb{R}^N$. On the half-space $\\mathbb{R}_+\\times\\mathbb{R}^N$, we consider systems of conjugate $(\\partial_t^2+\\Delta_{\\mathbf{x}})$-harmonic functions satisfying an appropriate uniform $L^1$ condition. We prove that the boundary values of such harmonic functions, which constitute the real Hardy space $H^1$, can be characterized in several different ways, namely by means of atoms, Riesz transforms, maximal functions or L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06607","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"}