  This paper deals with representing in concrete fashion those Hilbert spaces
that are vector subspaces of the Hardy spaces $H^p(\bb D^n) \ (1\le p\le
\infty)$ that remain invariant under the action of coordinate wise
multiplication by an $n$-tuple $(T_{B_1},\dots, T_{B_n})$ of operators where
each $B_i, \ 1\le i\le n,$ is a finite Blaschke factor on the open unit disc.
The critical point to be noted is that these $T_{B_i}$ are assumed to be weaker
than isometries as operators. Thus our main theorem extends the principal
result of \cite{LS} in the following three directions: $(i)$ from one to
several variables; $(ii)$ from multiplication with the coordinate function $z$
to an $n$-tuple of multiplication by finite Blaschke factors $B_i, \ 1\le i\le
n;$ $(iii)$ from vector subspaces of $H^2(\bb D)$ to the case of vector
subspaces of $H^p(\bb D^n), \ 1\le p\le \infty.$ We further derive a
generalization of Slocinski's well known Wold type decomposition of a pair of
doubly commuting isometries to the case of $n$-tuple of doubly commuting
operators whose actions are weaker than isometries.
