Hausdorff and quasi-Hausdorff matrices on spaces of analytic functions

We consider Hausdorff and quasi-Hausdorff matrices as operators on classical spaces of analytic functions such as the Hardy and the Bergman spaces, the Dirichlet space, the Bloch spaces and BMOA. When the generating sequence of the matrix is the moment sequence of a measure mu, we find the conditions on mu which are equivalent to the boundedness of the matrix on the various spaces.