{"paper":{"title":"Boundedness of Intrinsic Littlewood-Paley Functions on Musielak-Orlicz Morrey and Campanato Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Eiichi Nakai, Junqiang Zhang, Yiyu Liang","submitted_at":"2013-09-25T14:13:10Z","abstract_excerpt":"Let $\\varphi: {\\mathbb R^n}\\times [0,\\infty)\\to[0,\\infty)$ be such that $\\vz(x,\\cdot)$ is nondecreasing, $\\varphi(x,0)=0$, $\\varphi(x,t)>0$ when $t>0$, $\\lim_{t\\to\\infty}\\varphi(x,t)=\\infty$ and $\\vz(\\cdot,t)$ is a Muckenhoupt $A_\\infty({\\mathbb R^n})$ weight uniformly in $t$. Let $\\phi: [0,\\infty)\\to[0,\\infty)$ be nondecreasing. In this article, the authors introduce the Musielak-Orlicz Morrey space $\\mathcal M^{\\varphi,\\phi}(\\mathbb R^n)$ and obtain the boundedness on $\\mathcal M^{\\varphi,\\phi}(\\mathbb R^n)$ of the intrinsic Lusin area function $S_{\\alpha}$, the intrinsic $g$-function $g_{\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6512","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":""},"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"}