{"paper":{"title":"The Characterizations of Anisotropic Mixed-Norm Hardy Spaces on $\\mathbb{R}^n$ by Atoms and Molecules","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Aiting Wang, Wenhua Wang","submitted_at":"2022-03-15T02:58:57Z","abstract_excerpt":"Let $\\vec{p}\\in(0,\\,\\infty)^n$, $A$ be an expansive dilation on $\\mathbb{R}^n$,and $H^{\\vec{p}}_A({\\mathbb {R}}^n)$ be the anisotropic mixed-norm Hardy space defined via the non-tangential grand maximal function studied by \\cite{hlyy20}. In this paper, the authors establish new atomic and molecular decompositions of $H^{\\vec{p}}_A({\\mathbb {R}}^n)$. As an application, the authors obtain a boundedness criterion for a class of linear operators from $H^{\\vec{p}}_{A}(\\mathbb{R}^n)$ to $H^{\\vec{p}}_{A}(\\mathbb{R}^n)$. Part of results are still new even in the classical isotropic setting (in the cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.07611","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.07611/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}