{"paper":{"title":"Littlewood-Paley Characterizations of Anisotropic Hardy-Lorentz Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Jun Liu, Wen Yuan","submitted_at":"2016-01-20T11:32:26Z","abstract_excerpt":"Let $p\\in(0,1]$, $q\\in(0,\\infty]$ and $A$ be a general expansive matrix on $\\mathbb{R}^n$. Let $H^{p,q}_A(\\mathbb{R}^n)$ be the anisotropic Hardy-Lorentz spaces associated with $A$ defined via the non-tangential grand maximal function. In this article, the authors characterize $H^{p,q}_A(\\mathbb{R}^n)$ in terms of the Lusin-area function, the Littlewood-Paley $g$-function or the Littlewood-Paley $g_\\lambda^*$-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz space $L^{p,q}(\\mathbb{R}^n)$. All these characterizations are new even for the clas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05242","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"}