{"paper":{"title":"Atomic and Littlewood-Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Jun Liu, Long Huang, Wen Yuan","submitted_at":"2018-01-18T23:34:18Z","abstract_excerpt":"Let $\\vec{a}:=(a_1,\\ldots,a_n)\\in[1,\\infty)^n$, $\\vec{p}:=(p_1,\\ldots,p_n)\\in(0,\\infty)^n$ and $H_{\\vec{a}}^{\\vec{p}}(\\mathbb{R}^n)$ be the anisotropic mixed-norm Hardy space associated with $\\vec{a}$ defined via the non-tangential grand maximal function. In this article, via first establishing a Calder\\'{o}n-Zygmund decomposition and a discrete Calder\\'{o}n reproducing formula, the authors then characterize $H_{\\vec{a}}^{\\vec{p}}(\\mathbb{R}^n)$, respectively, by means of atoms, the Lusin area function, the Littlewood-Paley $g$-function or $g_{\\lambda}^\\ast$-function. The obtained Littlewood-P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06251","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"}