We study the condition that characterizes the symbols of bounded Hankel operators on the Bergman space of a strongly pseudoconvex domain and show that it is equivalent to BMO plus analytic. (Here we mean the Bergman metric BMO of Berger, Coburn and Zhu.) In the course of the proof we obtain new d -estimates that may be of independent interest. Some applications include a decomposition of BMO si...

For α > −1, let Aα denote the corresponding weighted Bergman space of the unit ball. For any self-adjoint subset G ⊂ L∞, let T(G) denote the C∗−subalgebra of B(Aα) generated by {Tf : f ∈ G}. Let CT(G) denote the commutator ideal of T(G). It was showed by D. Suárez (in 2004 for n = 1) and by the author (in 2006 for all n ≥ 1) that CT(L∞) = T(L∞) in the case α = 0. In this paper we show that in t...

Inspired by a result of Szőke, we give potential-theoretic characterizations the dimension Bergman space holomorphic sections restriction line bundle on $$\mathbb {P}^1$$ to some open set $$D\subset \mathbb .

The reproducing kernel function of a weighted Bergman space over domains in C is known explicitly in only a small number of instances. Here, we introduce a process of orthogonal norm expansion along a subvariety of codimension 1, which also leads to a series expansion of the reproducing kernel in terms of reproducing kernels defined on the subvariety. The problem of finding the reproducing kern...

We show that the classical Szasz analytic function SN (f)(x) is related to the Bergman kernel for the Bargmann-Fock space. Then we generalize this relation to any noncompact toric Kähler manifold, defining the generalized Szasz analytic function ShN (f)(x). Then we will prove the complete asymptotic expansion of ShN (f)(x) and its scaling limit property. As examples, we will compute the general...