{"paper":{"title":"New Hardy spaces of Musielak-Orlicz type and boundedness of sublinear operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Luong Dang Ky (MAPMO)","submitted_at":"2011-03-19T06:25:21Z","abstract_excerpt":"We introduce a new class of Hardy spaces $H^{\\varphi(\\cdot,\\cdot)}(\\mathbb R^n)$, called Hardy spaces of Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garc\\'ia-Cuerva, Str\\\"omberg, and Torchinsky. Here, $\\varphi: \\mathbb R^n\\times [0,\\infty)\\to [0,\\infty)$ is a function such that $\\varphi(x,\\cdot)$ is an Orlicz function and $\\varphi(\\cdot,t)$ is a Muckenhoupt $A_\\infty$ weight. A function $f$ belongs to $H^{\\varphi(\\cdot,\\cdot)}(\\mathbb R^n)$ if and only if its maximal function $f^*$ is so that $x\\mapsto \\varphi(x,|f^*(x)|)$ is integr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3757","kind":"arxiv","version":3},"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"}