{"paper":{"title":"Bloom type upper bounds in the product BMO setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Emil Vuorinen, Henri Martikainen, Kangwei Li","submitted_at":"2018-10-22T14:10:56Z","abstract_excerpt":"For a bounded singular integral $T_n$ in $\\mathbb{R}^n$ and a bounded singular integral $T_m$ in $\\mathbb{R}^m$ we prove that $$ \\| [T_n^1, [b, T_m^2]] \\|_{L^p(\\mu) \\to L^p(\\lambda)} \\lesssim_{[\\mu]_{A_p}, [\\lambda]_{A_p}} \\|b\\|_{\\operatorname{BMO}_{\\textrm{prod}}(\\nu)}, $$ where $p \\in (1,\\infty)$, $\\mu, \\lambda \\in A_p$ and $\\nu := \\mu^{1/p}\\lambda^{-1/p}$. Here $T_n^1$ is $T_n$ acting on the first variable, $T_m^2$ is $T_m$ acting on the second variable, $A_p$ stands for the bi-parameter weights of $\\mathbb{R}^n \\times \\mathbb{R}^m$ and $\\operatorname{BMO}_{\\textrm{prod}}(\\nu)$ is a weighte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09303","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"}