Carleson measures for Hardy and Bergman spaces in the quaternionic unit ball

We study a characterization of slice Carleson measures and of Carleson measures for the both the Hardy spaces $H^p(\mathbb{B})$ and the Bergman spaces ${\mathcal{A}}^p(\mathbb{B})$ of the quaternionic unit ball $\mathbb{B}$. In the case of Bergman spaces, the characterization is done in terms of the axially symmetric completion of a pseudohyperbolic disc in a complex plane. We also show that a characterization in terms of pseudohyperbolic balls is not possible.