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This paper deals with representing in concrete fashion those Hilbert spacesthat 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 wisemultiplication by an $n$-tuple $(T_{B_1},\dots, T_{B_n})$ of operators whereeach $B_i, \ 1\le i\le n,$ 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 weakerthan isometries as operators. Thus our main theorem extends the principalresult of \cite{LS} in the following three directions: $(i)$ from one toseveral variables; $(ii)$ from multiplication with the coordinate function $z$to an $n$-tuple of multiplication by finite Blaschke factors $B_i, \ 1\le i\len;$ $(iii)$ from vector subspaces of $H^2(\bb D)$ to the case of vectorsubspaces of $H^p(\bb D^n), \ 1\le p\le \infty.$ We further derive ageneralization of Slocinski's well known Wold type decomposition of a pair ofdoubly commuting isometries to the case of $n$-tuple of doubly commutingoperators whose actions are weaker than isometries.

Multivariable Sub-Hardy Hilbert Spaces Invariant under the action of $n$-tuple of Finite Blaschke factors