BEST CONSTANTS IN ROSENTHAL-TYPE INEQUALITIES AND THE KRUGLOV OPERATOR

• 成果类型: Article
• 署名作者: Astashkin, S. V.; Sukochev, F. A.
• 署名单位: Samara National Research University; University of New South Wales Sydney
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP529
• 发表日期: 2010
• 页码: 1986-2008
• 关键词: independent random-variables; sums; SEQUENCES; moment; NORMS

摘要

Let X be a symmetric Banach function space on [0, 1] with the Kruglov property, and let f = {f(k)}(k=1)(n), n > 1 be an arbitrary sequence of independent random variables in X. This paper presents sharp estimates in the deterministic characterization of the quantities parallel to Sigma(n)(k=1) f(k)parallel to(X), parallel to(Sigma(n)(k=1)vertical bar f(k)vertical bar(p))(1/p)parallel to(X), 1 <= p < infinity, in terms of the sum of disjoint copies of individual terms of f. Our method is novel and based on the important recent advances in the study of the Kruglov property through an operator approach made earlier by the authors. In particular, we discover that the sharp constants in the characterization above are equivalent to the norm of the Kruglov operator in X.