On harmonic Hardy spaces and area integrals. (English) Zbl 1063.31004

Stević, Stevo

J. Math. Soc. Japan 56, No. 2, 339-347 (2004).

The author proves several necessary and sufficient conditions for a harmonic function in the unit ball \(B\) of \(\mathbb R^n (n\geq 3)\) to belong to the Hardy space \(\mathcal H^p(B), 1<p<\infty\), of harmonic functions on \(B\). One such result is that \(u\in\mathcal H^p(B), 1<p<\infty\), if and only if \(u\) has the \(p\)-Lusin property with respect to a certain Stoltz domain.

Reviewer: Manfred Stoll (Columbia)

MSC:

31B05	Harmonic, subharmonic, superharmonic functions in higher dimensions
30D55	\(H^p\)-classes (MSC2000)
32A35	\(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables

Keywords:

harmonic functions; Hardy spaces; Stoltz domain