Quaternionic Möbius invariant Laplacian and quaternionic Möbius harmonic functions on the unit ball

We construct quaternionic Möbius ($\mathcal{QM}$ briefly) transformations on the quaternionic unit ball, which are used to define $\mathcal{QM}$-invariant Laplacian operator $\triangle$. A function annihilated by $\triangle$ is called $\mathcal{QM}$-harmonic. We prove that $\mathcal{QM}$-harmonic fu