On the structure of Bergman and poly-Bergman spaces

Let II be the upper half-plane in, consider the Bergman space, the subspace of all analytic functions fromL₂(II). The complete decomposition ofL₂(II) onto Bergman and Bergman type spaces of poly-analytic and poly-anti-analytic functions is obtained. The orthogonal Bergman type projections onto each of these subspaces are described. Connections with the Hardy spaces and the Szegö projections are established.This work was partially supported by CONACYT Project 3114P-E9607, México.