Mutual singularity of Riesz products on the unit sphere

Abstract: We prove analogs of Peyri`ere's mutual singularity theorem for standard and generalized Riesz products on the unit sphere of $\mathbb{C}<sup>n$, $n\ge 2$. As a corollary, we obtain an analog of Zygmund's dichotomy for the Riesz products under consideration.