Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 309-325

HARMONIC HARDY-ORLICZ SPACES

Tero Kilpeläinen, Pekka Koskela and Hiroaki Masaoka

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; tero.kilpelainen 'at' jyu.fi

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; pekka.j.koskela 'at' jyu.fi

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; hiroaki.h.masaoka 'at' jyu.fi
and Kyoto Sangyo University, Faculty of Science, Department of Mathematics
Kamigamo-Motoyama, Kitaku, Kyoto 603-8555, Japan; masaoka 'at' cc.kyoto-su.ac.jp

Abstract. Given an open hyperbolic Riemannian manifold, we show that various vector spaces of harmonic functions coincide if and only if they are finite dimensional.

2010 Mathematics Subject Classification: Primary 31C12; Secondary 31C35, 35J70.

Key words: P-Brelot harmonic space, harmonic Hardy-Orlicz space, minimal Martin boundary, harmonic measure.

Reference to this article: T. Kilpeläinen, P. Koskela and H. Masaoka: Harmonic Hardy-Orlicz spaces. Ann. Acad. Sci. Fenn. Math. 38 (2013), 309-325.

Full document as PDF file

doi:10.5186/aasfm.2013.3816