Strichartz's conjecture for the spinor bundle over the real hyperbolic space

Let $H^n(\mathbb R)$ denote the real hyperbolic space realized as the symmetric space $Spin_0(1,n)/Spin(n)$. In this paper, we provide a characterization for the image of the Poisson transform for $L^2$-sections of the spinor bundle over the boundary ${\partial H}^n(\mathbb R)$. As a consequence, we obtain an $L^2$ uniform estimate for the generalized spectral projections associated to the spinor bundle over $H^n(\mathbb R)$, thereby extending Strichartz's conjecture from the scalar case to the spinor setting.