{"paper":{"title":"The multi-parameter Hausdorff operators on $H^1$ and $L^p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Duong Quoc Huy, Luong Dang Ky","submitted_at":"2017-05-07T02:11:30Z","abstract_excerpt":"In the present paper, we characterize the nonnegative functions $\\varphi$ for which the multi-parameter Hausdorff operator $\\mathcal H_\\varphi$ generated by $\\varphi$ is bounded on the multi-parameter Hardy space $H^1(\\mathbb R\\times\\cdots\\times\\mathbb R)$ or $L^p(\\mathbb R^n)$, $p\\in [1,\\infty]$. The corresponding operator norms are also obtained. Our results improve some recent results in \\cite{FZ, LM2, LM3, We} and give an answer to an open question posted by Liflyand \\cite{Li}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02548","kind":"arxiv","version":2},"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"}