  We consider a class of vector-valued elliptic operators with unbounded
coefficients, coupled up to the first-order, in the Lebesgue space L^p(R^d;R^m)
with p in (1,\infty). Sufficient conditions to prove generation results of an
analytic C_0-semigroup T(t), together with a characterization of the domain of
its generator, are given. Some results related to the hypercontractivity and
the ultraboundedness of the semigroup are also established.
