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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
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