{"paper":{"title":"On General multilinear square function with non-smooth kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mahdi Hormozi, Qingying Xue, Zengyan Si","submitted_at":"2015-06-30T02:51:49Z","abstract_excerpt":"In this paper, we obtain some boundedness of the following general multilinear square functions $T$ with non-smooth kernels, which extend some known results significantly. $$ T(\\vec{f})(x)=\\big( \\int_{0}^\\infty \\big|\\int_{(\\mathbb{R}^n)^m}K_v(x,y_1,\\dots,y_m) \\prod_{j=1}^mf_{j}(y_j)dy_1,\\dots,dy_m\\big|^2\\frac{dv}{v}\\big)^{\\frac 12}. $$ The corresponding multilinear maximal square function $T^*$ was also introduced and weighted strong and weak type estimates for $T^*$ were given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08922","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"}