Analysis of some function spaces associated to Hankel operators (Q1362380)

A function in a Bergman space \(A^p(D)\) on a domain \(D\subseteq\mathbb{C}^n\) can be viewed as the restriction to \(\mathbb{C}^n\) of a function in a Hardy space on a domain \(D'\subseteq\mathbb{C}^{n+1}\). This point of view is developed, and a theory of ``real variable'' Bergman spaces is thereby established. A variety of applications are provided. In particular, a factorization theorem for the Bergman space is proved, as well as a characterization of the boundedness of the small Hankel operator.