Illinois Journal of Mathematics

Noncommutative extrapolation theorems and applications

Ying Hu

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In this paper, we prove some noncommutative analogues of Yano’s classical extrapolation theorem. Applying one of them to noncommutative martingales, we obtain a maximal inequality for noncommutative martingales from $L\log^2L$ to $L_1$. Moreover, the exponent $2$ is optimal. We also obtain the noncommutative analogue of the classical theorem of Burkholder and Chow on the iterations of two conditional expectations.

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Illinois J. Math., Volume 53, Number 2 (2009), 463-482.

First available in Project Euclid: 23 February 2010

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Zentralblatt MATH identifier

Primary: 46L53: Noncommutative probability and statistics 65L06: Multistep, Runge-Kutta and extrapolation methods
Secondary: 46L51: Noncommutative measure and integration 46L52: Noncommutative function spaces 60G42: Martingales with discrete parameter


Hu, Ying. Noncommutative extrapolation theorems and applications. Illinois J. Math. 53 (2009), no. 2, 463--482. doi:10.1215/ijm/1266934788.

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