WEAK PRODUCTS, HANKEL OPERATORS, AND INVARIANT SUBSPACES

When studying the Hardy space of analytic functions on a region, it
is natural to view it as part of the family of Hp-spaces, and investigate
how properties of the functions and operators on these spaces change as
the parameter p changes. For reproducing kernel Hilbert spaces like the
Dirichlet space of the unit disc or the Drury-Arveson space of the unit
ball of Cd it is unclear what a natural class of related spaces should be.
The weak product H  H and the space of Hankel symbols X(H) can
be associated with a large class of reproducing kernel Hilbert spaces.
They may be considered to be the analogs of H1 and BMOA from the
Hardy space theory.
In this talk I will present details of this set-up with a view of what
they say about the Dirichlet- and Drury-Arveson spaces.