{"paper":{"title":"Best constants in Rosenthal-type inequalities and the Kruglov operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. A. Sukochev, S. V. Astashkin","submitted_at":"2010-11-05T12:26:58Z","abstract_excerpt":"Let $X$ be a symmetric Banach function space on $[0,1]$ with the Kruglov property, and let $\\mathbf{f}=\\{f_k\\}_{{k=1}}^n$, $n\\ge1$ be an arbitrary sequence of independent random variables in $X$. This paper presents sharp estimates in the deterministic characterization of the quantities \\[\\Biggl\\|\\sum_{{k=1}}^nf_k\\Biggr\\|_X,\\Biggl\\|\\Biggl(\\sum_{{k=1}}^n|f_k|^p\\Biggr)^{1/p}\\Biggr\\|_X,\\qquad 1\\leq p<\\infty,\\] in terms of the sum of disjoint copies of individual terms of $\\mathbf{f}$. Our method is novel and based on the important recent advances in the study of the Kruglov property through an op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1381","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"}