Mixed-norm inequalities and operator space Lp embedding theory - Junge, Marius; Parcet, Javier (Memoirs of the American Mathematical Society, 2009)
The authors prove a noncommutative analogue of this inequality for sums of free random variables over a given von Neumann subalgebra. This formulation leads to new classes of noncommutative function spaces which appear in quantum probability as square functions, conditioned square functions and maximal functions.