  Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a
normal faithful state $\varphi$, and let $\mathcal{A}$ be maximal subdiagonal
subalgebra of $\mathcal{M}$ and $1\le p<\8$. We prove a
Beurling-Blecher-Labuschagne type theorem for $\mathcal{A}$-invariant subspaces
of Haagerup noncommutative $L^p(\mathcal{M})$ and give a characterization of
outer operators in Haagerup noncommutative $H^{p}$-spaces associated with
$\mathcal{A}$.
