Distributional boundary values in . V
In this note we establish a vector-valued version of Beurling’s theorem (the Lax-Halmos theorem) for the polydisc. As an application of the main result, we provide necessary and sufficient conditions for the “weak” completion problem in .
We study Hardy, Bergman, Bloch, and BMO spaces on convex domains of finite type in -dimensional complex space. Duals of these spaces are computed. The essential features of complex domains of finite type, that make these theorems possible, are isolated.