The Dirichlet space: A Survey

Details The Dirichlet space: A Survey The Dirichlet space: A Survey

2010-08-31

arxiv.org/abs/1008.5342v4

New York J. Math. 17A (2011), 45--86

Mathematics

Complex Variables

35 pages, typoes corrected, some open problems added

Scientific paper

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.

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