  We introduce Hardy spaces for martingales with respect to continuous
filtration for von Neumann algebras. In particular we prove the analogues of
the Burkholder/Gundy and Burkholder/Rosenthal inequalities in this setting. The
usual arguments using stopping times in the commutative case are replaced by
tools from noncommutative function theory and allow us to obtain the analogue
of the Feffermann-Stein duality and prove a noncommutative Davis decomposition.
