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

Chang, Der-Chen

Forum Math. 6, No. 1, 65-81 (1994).

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