✦ LIBER ✦

Little Bloch Functions, Symmetric Pluriharmonic Measures, and Zygmund's Dichotomy

✍ Scribed by Evgueni Doubtsov

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 226 KB
Volume: 170
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1999.3510

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✦ Synopsis

We introduce special Riesz products on the complex sphere and prove Zygmund's dichotomy for such products. Given d # Z + , this construction yields a d-pluriharmonic measure + such that all slices of + 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.