{"paper":{"title":"Weighted weak type endpoint estimates for the composition of Calderon-Zygmund operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guoen Hu","submitted_at":"2018-06-01T11:18:47Z","abstract_excerpt":"Let $T_1$, $T_2$ be two Calder\\'on-Zygmund operators and $T_{1,\\,b}$ be the commutator of $T_1$ with symbol $b\\in {\\rm BMO}(\\mathbb{R}^n)$. In this paper, the author prove that, the composite operator $T_1T_2$ satisfies the following estimate: for $\\lambda>0$ and weight $w\\in A_1(\\mathbb{R}^n)$, \\begin{eqnarray*}&&w\\big(\\{x\\in\\mathbb{R}^n:\\,|T_{1} T_2f(x)|>\\lambda\\}\\big)\\\\ &&\\quad\\lesssim [w]_{A_1}[w]_{A_{\\infty}}\\log ({\\rm e}+[w]_{A_{\\infty}}\\big) \\int_{\\mathbb{R}^n}\\frac{|f(x)|}{\\lambda}\\log \\Big({\\rm e}+\\frac{|f(x)|}{\\lambda}\\Big)w(x)dx,\\nonumber \\end{eqnarray*} and the composite operator $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00289","kind":"arxiv","version":4},"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"}