Differentiability of bizonal positive definite kernels on complex spheres

We prove that any continuous function with domain {z∈C:|z|⩽1} that generates a bizonal positive definite kernel on the unit sphere in Cq, q⩾3, is continuously differentiable in {z∈C:|z|<1} up to order q−2, with respect to both z and z¯. In particular, the partial derivatives of the function with respect to x=Rez and y=Imz exist and are continuous in {z∈C:|z|<1} up to the same order.