  There exist several interesting results in the literature on subnormal
operator tuples having their spectral properties tied to the geometry of
strictly pseudoconvex domains or to that of bounded symmetric domains in
$\C^n$. We introduce a class $\Omega^{(n)}$ of convex domains in $\C^n$ which,
for $n \geq 2$, is distinct from the class of strictly pseudoconvex domains and
the class of bounded symmetric domains and which lends itself for the
application of the theories related to the abstract inner function problem and
the $\bar \partial$-Neumann problem, allowing us to make a number of
interesting observations about certain subnormal operator tuples associated
with the members of the class $\Omega^{(n)}$.
