an:00575620
Zbl 0802.32013
Krantz, Steven G.; Li, Song-Ying
A note on Hardy spaces and functions of bounded mean oscillation on domains in \(\mathbb{C}^ n\)
EN
Mich. Math. J. 41, No. 1, 51-71 (1994).
00019659
1994
j
32A35 32A37
BMOA; Hardy space; holomorphic functions; pseudoconvex domain; finite type
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 \(\text{BMOA}(\Omega)\).
P.Z.Agranovich (Khar'kov)