{"paper":{"title":"Norm of the Hausdorff operator on the real Hardy space $H^1(\\mathbb R)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ha Duy Hung, Luong Dang Ky, Thai Thuan Quang","submitted_at":"2017-02-12T04:17:28Z","abstract_excerpt":"Let $\\varphi$ be a nonnegative integrable function on $(0,\\infty)$. It is well-known that the Hausdorff operator $\\mathcal H_\\varphi$ generated by $\\varphi$ is bounded on the real Hardy space $H^1(\\mathbb R)$. The aim of this paper is to give the exact norm of $\\mathcal H_\\varphi$. More precisely, we prove that $$\\|\\mathcal H_\\varphi\\|_{H^1(\\mathbb R)\\to H^1(\\mathbb R)}= \\int_0^\\infty \\varphi(t)dt.$$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03486","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"}