  We prove the noncommutative Davis decomposition for the column Hardy space
$\H_p^c$ for all $0<p\leq 1$. A new feature of our Davis decomposition is a
simultaneous control of $\H_1^c$ and $\H_q^c$ norms for any noncommutative
martingale in $\H_1^c \cap \H_q^c$ when $q\geq 2$. As applications, we show
that the Burkholder/Rosenthal inequality holds for bounded martingales in a
noncommutative symmetric space associated with a function space $E$ that is
either an interpolation of the couple $(L_p, L_2)$ for some $1<p<2$ or is an
interpolation of the couple $(L_2, L_q)$ for some $2<q<\infty$. We also obtain
the corresponding $\Phi$-moment Burkholder/Rosenthal inequality for Orlicz
functions that are either $p$-convex and $2$-concave for some $1<p<2$ or are
$2$-convex and $q$-concave for some $2<q<\infty$.
