In this paper we study the duality of the harmonic spaces on the annulus Ω = Ω1 \Ω − between two pseudoconvex domains with Ω− ⊂⊂ Ω1 in Cn and the Bergman spaces on Ω−. We show that on the annulus Ω, the space of harmonic forms for the critical case on (0, n−1)-forms is infinite dimensional and it is dual to the the Bergman space on the pseudoconvex domain Ω−. The duality is further identified e...

Let Π = {z ∈ C : Imz > 0} be the upper half-plane in the complex plane. This paper characterizes the bounded products of differentiation operator and composition operator acting from the weighted Bergman space Aα(Π) to the weighted-type space A∞(Π) and the Bloch-type space B∞(Π). Mathematics Subject Classification: Primary 47B38; Secondary 47B33, 47B37

The orthogonal projection from a Sobolev space WS(Q) onto the subspace of holomorphic functions is studied. This analogue of the Bergman projection is shown to satisfy regularity estimates in higher Sobolev norms when ß is a smooth bounded strictly pseudoconvex domain in C". The Bergman projection P0: L2(ü) -» L2(S2) n {holomorphic functions}, where S2 c C" is a smooth bounded domain, has prove...

Let Ω = G/K be a bounded symmetric domain in a complex vector space V with the Lebesgue measure dm(z) and the Bergman reproducing kernel h(z, w). Let dμα(z) = h(z, z̄) dm(z), α > −1, be the weighted measure on Ω. The group G acts unitarily on the space L(Ω, μα) via change of variables together with a multiplier. We consider the discrete parts, also called the relative discrete series, in the irr...