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September 2010 Best constants in Rosenthal-type inequalities and the Kruglov operator
S. V. Astashkin, F. A. Sukochev
Ann. Probab. 38(5): 1986-2008 (September 2010). DOI: 10.1214/10-AOP529

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=1nfkX, ‖(∑k=1n|fk|p)1/pX, 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.

Citation

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S. V. Astashkin. F. A. Sukochev. "Best constants in Rosenthal-type inequalities and the Kruglov operator." Ann. Probab. 38 (5) 1986 - 2008, September 2010. https://doi.org/10.1214/10-AOP529

Information

Published: September 2010
First available in Project Euclid: 17 August 2010

zbMATH: 1211.46008
MathSciNet: MR2722792
Digital Object Identifier: 10.1214/10-AOP529

Subjects:
Primary: 46B09 , 60G50

Keywords: Kruglov property , Rosenthal inequality , symmetric function spaces

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 5 • September 2010
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