{"paper":{"title":"Weak type operator Lipschitz and commutator estimates for commuting tuples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Dmitriy Zanin, Fedor Sukochev, Martijn Caspers","submitted_at":"2017-03-09T00:59:23Z","abstract_excerpt":"Let $f: \\mathbb{R}^d \\to\\mathbb{R}$ be a Lipschitz function. If $B$ is a bounded self-adjoint operator and if $\\{A_k\\}_{k=1}^d$ are commuting bounded self-adjoint operators such that $[A_k,B]\\in L_1(H),$ then $$\\|[f(A_1,\\cdots,A_d),B]\\|_{1,\\infty}\\leq c(d)\\|\\nabla(f)\\|_{\\infty}\\max_{1\\leq k\\leq d}\\|[A_k,B]\\|_1,$$ where $c(d)$ is a constant independent of $f$, $\\mathcal{M}$ and $A,B$ and $\\|\\cdot\\|_{1,\\infty}$ denotes the weak $L_1$-norm. If $\\{X_k\\}_{k=1}^d$ (respectively, $\\{Y_k\\}_{k=1}^d$) are commuting bounded self-adjoint operators such that $X_k-Y_k\\in L_1(H),$ then $$\\|f(X_1,\\cdots,X_d)-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03089","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"}