The Dirichlet space: A Survey
Complex Variables
2011-09-13 v4 Operator Algebras
Abstract
In this paper we survey many results on the Dirichlet space of analytic functions. Our focus is more on the classical Dirichlet space on the disc and not the potential generalizations to other domains or several variables. Additionally, we focus mainly on certain function theoretic properties of the Dirichlet space and omit covering the interesting connections between this space and operator theory. The results discussed in this survey show what is known about the Dirichlet space and compares it with the related results for the Hardy space.
Cite
@article{arxiv.1008.5342,
title = {The Dirichlet space: A Survey},
author = {Nicola Arcozzi and Richard Rochberg and Eric Sawyer and Brett Wick},
journal= {arXiv preprint arXiv:1008.5342},
year = {2011}
}
Comments
35 pages, typoes corrected, some open problems added