{"paper":{"title":"Estimates for Parametric Marcinkiewicz Integrals on Musielak-Orlicz Hardy Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Baode Li, Bo Li, Xiaoli Qiu, Xiong Liu","submitted_at":"2018-07-24T06:13:46Z","abstract_excerpt":"Let $\\varphi:\\mathbb{R}^n\\times[0,\\,\\infty) \\rightarrow [0,\\,\\infty)$ satisfy that $\\varphi(x,\\,\\cdot)$, for any given $x\\in\\mathbb{R}^n$, is an Orlicz function and $\\varphi(\\cdot\\,,t)$ is a Muckenhoupt $A_\\infty$ weight uniformly in $t\\in(0,\\,\\infty)$. The Musielak-Orlicz Hardy space $H^\\varphi(\\mathbb{R}^n)$ generalizes both of the weighted Hardy space and the Orlicz Hardy space and hence has a wide generality. In this paper, the authors first prove the completeness of both of the Musielak-Orlicz space $L^\\varphi(\\mathbb{R}^n)$ and the weak Musielak-Orlicz space $WL^\\varphi(\\mathbb{R}^n)$. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08921","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"}