论文标题
重新访问Marcinkiewicz定理非交换最大函数
Revisiting the Marcinkiewicz theorem for non commutative maximal functions
论文作者
论文摘要
我们提供了Marcinkiewicz插值定理的替代证明，用于非交换性最大函数和正图，并略微完善了该陈述的早期版本。主要的新颖性是它可以替代Martingale在$ l_p $，$ 1 <p \ leq \ infty $中的最大功能，在数值常数上几乎没有损失。对于非正图，上述定理失败，但我们仍然可以通过削弱我们考虑的最大规范来获得一些插值结果。
We give an alternative proof of a Marcinkiewicz interpolation theorem for non commutative maximal functions and positive maps, slightly refining earlier versions of the statement. The main novelty is that it provides a substitute for the maximal function of a martingale in $L_p$, $1<p\leq \infty$, losing very little on numerical constants. For non positive maps, the above mentioned theorem fails but we can still obtain some interpolation results by weakening the maximal norms that we consider.
