  Let $\Omega=G/K$ be a bounded symmetric domain and $S=K/L$ its Shilov
boundary. We consider the action of $G$ on sections of a homogeneous line
bundle over $\Omega$ and the corresponding eigenspaces of $G$-invariant
differential operators. The Poisson transform maps hyperfunctions on the $S$ to
the eigenspaces. We characterize the image in terms of twisted Hua operators.
For some special parameters the Poisson transform is of Szeg\"o type mapping
into the relative discrete series; we compute the corresponding elements in the
discrete series.
