Resumen de Revisiting the Marcinkiewicz theorem for non-commutative maximal functions
We give an alternative proof of a Marcinkiewicz interpolation theorem for non-commutative maximal functions and positive maps and refine earlier versions of the statement. The main novelty is that it provides a substitute for the maximal function of a martingale in Lp, 1 < p 6 ∞, 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 norm that we consider.
