Noncommutative weak Orlicz spaces and martingale inequalities
Volume 204 / 2011
Studia Mathematica 204 (2011), 195-212
MSC: Primary 46L53; Secondary 60G42.
DOI: 10.4064/sm204-3-1
Abstract
This paper is devoted to the study of noncommutative weak Orlicz spaces and martingale inequalities. The Marcinkiewicz interpolation theorem is extended to include noncommutative weak Orlicz spaces as interpolation classes. As an application, we prove the weak type $\varPhi $-moment Burkholder–Gundy inequality for noncommutative martingales through establishing a weak type $\varPhi $-moment noncommutative Khinchin inequality for Rademacher random variables.
