{"paper":{"title":"Weighted Endpoint Estimates for Commutators of Calder\\'on-Zygmund Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Luong Dang Ky, Yiyu Liang","submitted_at":"2015-10-20T12:18:20Z","abstract_excerpt":"Let $\\delta\\in(0,1]$ and $T$ be a $\\delta$-Calder\\'on-Zygmund operator. Let $w$ be in the Muckenhoupt class $A_{1+\\delta/n}({\\mathbb R}^n)$ satisfying $\\int_{{\\mathbb R}^n}\\frac {w(x)}{1+|x|^n}\\,dx<\\infty$. When $b\\in{\\rm BMO}(\\mathbb R^n)$, it is well known that the commutator $[b, T]$ is not bounded from $H^1(\\mathbb R^n)$ to $L^1(\\mathbb R^n)$ if $b$ is not a constant function. In this article, the authors find out a proper subspace ${\\mathop\\mathcal{BMO}_w({\\mathbb R}^n)}$ of $\\mathop\\mathrm{BMO}(\\mathbb R^n)$ such that, if $b\\in {\\mathop\\mathcal{BMO}_w({\\mathbb R}^n)}$, then $[b,T]$ is bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05855","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"}