New York Journal of Mathematics
Volume 17a (2011) 45-86


Nicola Arcozzi, Richard Rochberg, Eric T. Sawyer, and Brett D. Wick

The Dirichlet space: a survey

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Published: January 30, 2011
Keywords: Analytic Dirichlet space, interpolating sequences, capacity, Carleson measures
Subject: 30C85, 31C25, 46E22, 30E05

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.


N.A.'s work partially supported by the COFIN project Analisi Armonica, funded by the Italian Minister for Research. R.R.'s work supported by the National Science Foundation under Grant No. 0700238. E.S.'s work supported by the National Science and Engineering Council of Canada. B.W.'s work supported by the National Science Foundation under Grant No. 1001098.

Author information

Nicola Arcozzi:
N. Arcozzi, Dipartimento do Matematica, Universita di Bologna, 40127 Bologna, ITALY

Richard Rochberg:
R. Rochberg, Department of Mathematics, Washington University, St. Louis, MO 63130, U.S.A

Eric T. Sawyer:
E. T. Sawyer, Department of Mathematics & Statistics, McMaster University, Hamilton, Ontairo, L8S 4K1, CANADA

Brett D. Wick:
B. D. Wick, School of Mathematics, Georgian Institute of Technology, 686 Cherry, Street, Atlanta, GA USA 30332-0160