Mutual singularity of Riesz products on the unit sphere

Abstract

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

8 pages