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Best constants in Rosenthal-type inequalities and the Kruglov operator | | S. V. Astashkin
; F. A. Sukochev
; | | Date: |
5 Nov 2010 | | Abstract: | Let $X$ be a symmetric Banach function space on $[0,1]$ with the Kruglov
property, and let $mathbf{f}={f_k}_{{k=1}}^n$, $nge1$ 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_kBiggr|_X,Biggl|Biggl(sum_{{k=1}}^n|f_k|^pBiggr)^{1/p}Biggr|_X,qquad
1leq 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 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
$X$. | | Source: | arXiv, 1011.1381 | | Services: | Forum | Review | PDF | Favorites | |
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