{"paper":{"title":"Regularity and continuity of local Multilinear Maximal type operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Feng Liu, Jarod Hart, Qingying Xue","submitted_at":"2018-06-18T12:32:29Z","abstract_excerpt":"This paper will be devoted to study the regularity and continuity properties of the following local multilinear fractional type maximal operators, $$\\mathfrak{M}_{\\alpha,\\Omega}(\\vec{f})(x)=\\sup\\limits_{0<r<{\\rm dist}(x,\\Omega^c)}\\frac{r^\\alpha}{|B(x,r)|^m}\\prod\\limits_{i=1}^m\\int_{B(x,r)}|f_i(y)|dy,\\quad \\hbox{for \\ }0\\leq\\alpha<mn,$$ where $\\Omega$ is a subdomain in $\\mathbb{R}^n$, $\\Omega^c=\\mathbb{R}^n\\backslash\\Omega$ and $B(x,r)$ is the ball in $\\mathbb{R}^n$ centered at $x$ with radius $r$. Several new pointwise estimates for the derivative of the local multilinear maximal function $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06627","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"}