Characterization of Poisson integrals on non-tube bounded symmetric domains

Abdelhamid Boussejra (1) , Khalid Koufany (2)

1 Département de Mathématiques [Kénitra]
2 IECN - Institut Élie Cartan de Nancy

We characterize the $L^p$-range, $1 < p < +\infty$, of the Poisson transform on the Shilov boundary for non-tube bounded symmetric domains. We prove that this range is a Hua-Hardy type space for harmonic functions satisfying a Hua system.

Domaines: Théorie des représentations [math.RT]

Abdelhamid Boussejra, Khalid Koufany. Characterization of Poisson integrals on non-tube bounded symmetric domains. Journal de Mathématiques Pures et Appliquées, 2007, 87, pp.438-451. ⟨hal-00095481⟩