zbMATH — the first resource for mathematics

A note on Hardy spaces and functions of bounded mean oscillation on domains in \(\mathbb{C}^ n\). (English) Zbl 0802.32013
Let \(\Omega\) be a smoothly bounded domain in \(\mathbb{C}^ n\), \(n\geq 2\) and \(H^ 1(\Omega)\) be Hardy space of holomorphic functions on \(\Omega\). Let, further, \(\text{BMOA}(\Omega)\) be the space of holomorphic functions in \(H^ 1(\Omega)\) whose boundary values are in \(\text{BMO}(\partial\Omega)\).
The following theorem is the main result of this paper.
Theorem 1.1. Let \(\Omega\) be a bounded strongly pseudoconvex domain in \(\mathbb{C}^ n\), or a bounded pseudoconvex domain of finite type in \(\mathbb{C}^ 2\). Then the dual of \(H^ 1(\Omega)\) is \(\text{BMOA}(\Omega)\).

32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
Full Text: DOI