2005 Volume 31 Issue 2 Pages 281-343
Let G be a real rank one connected semisimple Lie group with finite center. We introduce a real Hardy space H1 (G//K) on G as the space consisting of all K-bi-invariant functions f on G whose radial maximal functions Mφf are integrable on G. We shall obtain a relation between H1 (G//K) and H1(R), the real Hardy space on the real line R, via the Abel transform on G and give a characterization of H1 (G//K).