Best constants in Rosenthal-type inequalities and the Kruglov operator
S. V. Astashkin and F. A. Sukochev
Source: Ann. Probab. Volume 38, Number 5
(2010), 1986-2008.
Abstract
Let X be a symmetric Banach function space on [0, 1] with the Kruglov property, and let f={fk}k=1n, n≥1 be an arbitrary sequence of independent random variables in X. This paper presents sharp estimates in the deterministic characterization of the quantities
‖∑k=1nfk‖X, ‖(∑k=1n|fk|p)1/p‖X, 1≤p<∞,
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.
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1282053778
Digital Object Identifier: doi:10.1214/10-AOP529
Zentralblatt MATH identifier: 05793428
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