On the structure of Bergman and poly-Bergman spaces

Abstract

Let II be the upper half-plane inℂ, consider the Bergman space $$\mathcal{A}^2 (II)$$ , the subspace of all analytic functions fromL 2(II). The complete decomposition ofL 2(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 Szego projections are established.