Little Bloch Functions, Symmetric Pluriharmonic Measures, and Zygmundʹs Dichotomy

We introduce special Riesz products on the complex sphere and prove Zygmundʹs dichotomy for such products. Given d∈Z+, this construction yields a d-pluriharmonic measure μ such that all slices of μ are singular and uniformly symmetric. In particular, there exist non-constant little Bloch inner functions in the complex ball. Further little Bloch applications are given.