  Let $\A$ be a finite subdiagonal algebra in Arveson's sense. Let $H^p(\A)$ be
the associated noncommutative Hardy spaces, $0<p\le\8$. We extend to the case
of all positive indices most recent results about these spaces, which include
notably the Riesz, Szeg\"o and inner-outer type factorizations. One new tool of
the paper is the contractivity of the underlying conditional expectation on
$H^p(\A)$ for $p<1$.
