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~2 L 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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