{"paper":{"title":"The $n$-linear embedding theorem for dyadic rectangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hitoshi Tanaka, Kozo Yabuta","submitted_at":"2017-10-23T01:50:02Z","abstract_excerpt":"Let $\\sg_i$, $i=1,\\ldots,n$, denote reverse doubling weights on $\\R^d$, let $\\cdr(\\R^d)$ denote the set of all dyadic rectangles on $\\R^d$ (Cartesian products of usual dyadic intervals) and let $K:\\,\\cdr(\\R^d)\\to[0,\\8)$ be a~map. In this paper we give the $n$-linear embedding theorem for dyadic rectangles. That is, we prove the $n$-linear embedding inequality for dyadic rectangles \\[ \\sum_{R\\in\\cdr(\\R^d)} K(R)\\prod_{i=1}^n\\lt|\\int_{R}f_i\\,{\\rm d}\\sg_i\\rt| \\le C \\prod_{i=1}^n \\|f_i\\|_{L^{p_i}(\\sg_i)} \\] can be characterized by simple testing condition \\[ K(R)\\prod_{i=1}^n\\sg_i(R) \\le C \\prod_{i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08059","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"}