## The dual of Hardy spaces on a bounded domain in $$\mathbb{R}^ n$$.(English)Zbl 0803.42014

In this interesting paper Hardy spaces on a bounded Lipschitz domain $$\Omega\subset\mathbb{R}^ n$$ are studied. Whereas quite a well-developed theory of Hardy spaces on $$\mathbb{R}^ n$$ is available, the development of its local modification has been considerably slower. In the paper under review, two different definitions of a local Hardy space $$h^ p(\Omega)$$, $$0< p\leq 1$$, are treated, and the dual spaces to both are found. These dual spaces are two different adaptations to a domain of the BMO space in $$\mathbb{R}^ n$$.
Reviewer: L.Pick (Praha)

### MSC:

 42B30 $$H^p$$-spaces

### Keywords:

dual space; local Hardy space; BMO
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