{"paper":{"title":"New Real-Variable Characterizations of Musielak-Orlicz Hardy Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Jizheng Huang, Yiyu Liang","submitted_at":"2012-01-19T14:06:45Z","abstract_excerpt":"Let $\\varphi: {\\mathbb R^n}\\times [0,\\infty)\\to[0,\\infty)$ be such that $\\varphi(x,\\cdot)$ is an Orlicz function and $\\varphi(\\cdot,t)$ is a Muckenhoupt $A_\\infty({\\mathbb R^n})$ weight. The Musielak-Orlicz Hardy space $H^{\\varphi}(\\mathbb R^n)$ is defined to be the space of all $f\\in{\\mathcal S}'({\\mathbb R^n})$ such that the grand maximal function $f^*$ belongs to the Musielak-Orlicz space $L^\\varphi(\\mathbb R^n)$. Luong Dang Ky established its atomic characterization. In this paper, the authors establish some new real-variable characterizations of $H^{\\varphi}(\\mathbb R^n)$ in terms of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4062","kind":"arxiv","version":4},"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"}