Mutual singularity of Riesz products on the unit sphere

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We prove analogs of Peyrière’s mutual singularity theorem for standard and generalized Riesz products on the unit sphere of C n \mathbb {C}^n , n ≥ 2 n\ge 2 . As a corollary, we obtain an analog of Zygmund’s dichotomy for the Riesz products under consideration.