Abstract
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.
Citation
Ying Hu. "Noncommutative extrapolation theorems and applications." Illinois J. Math. 53 (2) 463 - 482, Summer 2009. https://doi.org/10.1215/ijm/1266934788
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