{"paper":{"title":"Intrinsic Structures of Certain Musielak-Orlicz Hardy Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Jun Cao, Liguang Liu, Wen Yuan","submitted_at":"2017-07-19T07:42:36Z","abstract_excerpt":"For any $p\\in(0,\\,1]$, let $H^{\\Phi_p}(\\mathbb{R}^n)$ be the Musielak-Orlicz Hardy space associated with the Musielak-Orlicz growth function $\\Phi_p$, defined by setting, for any $x\\in\\mathbb{R}^n$ and $t\\in[0,\\,\\infty)$,\n  $$ \\Phi_{p}(x,\\,t):= \\begin{cases} \n\\frac{t}{\\log(e+t)+[t(1+|x|)^n]^{1-p}} & \\qquad \\text{when } n(1/p-1)\\notin \\mathbb{N} \\cup \\{0\\}; \\\\\n\\frac{t}{\\log(e+t)+[t(1+|x|)^n]^{1-p}[\\log(e+|x|)]^p} & \\qquad \\text{when } n(1/p-1)\\in \\mathbb{N}\\cup\\{0\\},\\\\ \\end{cases} $$ which is the sharp target space of the bilinear decomposition of the product of the Hardy space $H^p(\\mathbb{R}^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05966","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"}