Revisiting the Marcinkiewicz theorem for non commutative maximal functions

Léonard Cadilhac (1) , Éric Ricard (2)

1 SU - Sorbonne Université
2 UNICAEN - Université de Caen Normandie

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

Domaines: Mathématiques [math]

Léonard Cadilhac, Éric Ricard. Revisiting the Marcinkiewicz theorem for non commutative maximal functions. 2023. ⟨hal-03924923⟩