Admissible functions for the Dirichlet space
Volume 198 / 2010
Studia Mathematica 198 (2010), 147-156
MSC: Primary 30C15; Secondary 30J10, 30H10, 31C25.
DOI: 10.4064/sm198-2-3
Abstract
Zero sets and uniqueness sets of the classical Dirichlet space $\mathcal{D}$ are not completely characterized yet. We define the concept of admissible functions for the Dirichlet space and then apply them to obtain a new class of zero sets for $\mathcal{D}$. Then we discuss the relation between the zero sets of $\mathcal{D}$ and those of $\mathcal{A}^\infty$.
