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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 $$\text{BMOA}(\Omega)$$.

##### MSC:
 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))
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