{"paper":{"title":"Regularity and continuity of the multilinear strong maximal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Feng Liu, Kozo Yabuta, Qingying Xue","submitted_at":"2018-01-30T02:35:39Z","abstract_excerpt":"Let $m\\ge 1$, in this paper, our object of investigation is the regularity and and continuity properties of the following multilinear strong maximal operator $${\\mathscr{M}}_{\\mathcal{R}}(\\vec{f})(x)=\\sup_{\\substack{R \\ni x R\\in\\mathcal{R}}}\\prod\\limits_{i=1}^m\\frac{1}{|R|}\\int_{R}|f_i(y)|dy,$$ where $x\\in\\mathbb{R}^d$ and $\\mathcal{R}$ denotes the family of all rectangles in $\\mathbb{R}^d$ with sides parallel to the axes. When $m=1$, denote $\\mathscr{M}_{\\mathcal{R}}$ by $\\mathcal {M}_{\\mathcal{R}}$.Then, $\\mathcal {M}_{\\mathcal{R}}$ coincides with the classical strong maximal function initia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09828","kind":"arxiv","version":2},"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"}