On Poisson transforms for spinors

Let (Formula presented) be a spinor representation of Spin (n) and let (σ, Vσ) be a spinor representation of Spin(n − 1) that occurs in the restriction (Formula presented). We consider the real hyperbolic space H n (R) as the rank one symmetric space Spin 0 (1, n)/ Spin (n) and the spinor bundle (Formula presented) as the homogeneous bundle Spin (Formula presented). In this paper we characterize eigenspinors of the algebra of invariant differential operators acting on 6H n (R) which can be written as the Poisson transform of L p -sections of the bundle Spin (Formula presented) over the boundary (Formula presented).