Bounded holomorphic functions with multiple sheeted pluripolar hulls
Volume 175 / 2006
Studia Mathematica 175 (2006), 233-247
MSC: Primary 32D15, 32U30; Secondary 31C10, 30C85.
DOI: 10.4064/sm175-3-3
Abstract
We describe compact subsets $K$ of $\partial\mathbb D$ and $\mathbb R$ admitting holomorphic functions $f$ with the domains of existence equal to ${\mathbb C}\setminus K$ and such that the pluripolar hulls of their graphs are infinitely sheeted. The paper is motivated by a recent paper of Poletsky and Wiegerinck.
