{"paper":{"title":"Endpoint estimates for the commutators of multilinear Calder\\'{o}n-Zygmund operators with Dini type kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Qingying Xue, Zhengyang Li","submitted_at":"2016-01-10T02:56:00Z","abstract_excerpt":"Let $T_{\\vec{b}}$ and $T_{\\Pi b}$ be the commutators in the $j$-th entry and iterated commutators of the multilinear Calder\\'{o}n-Zygmund operators, respectively. It was well-known that $T_{\\vec{b}}$ and $T_{\\Pi b}$ were not of weak type $(1,1)$ and $(H^1, L^1)$, but they did satisfy certain endpoint $L\\log L$ type estimates. In this paper, our aim is to give more natural sharp endpoint results. We show that $T_{\\vec{b}}$ and $T_{\\Pi b}$ are bounded from product Hardy space $H^1\\times\\cdot\\cdot\\cdot\\times H^1$ to weak $L^{\\frac{1}{m},\\infty}$ space, whenever the kernel satisfies a class of Din"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02173","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"}