Abstract
Some characterizations of the so-called Dirichlet-type spaces D(μ) are given. First we characterize D(μ) by means of the derivative free integral and of the mean oscillation in the Bergman metric. We then obtain a characterization for D(μ) that makes use of high-order derivative. Finally, as the main result of this article, we establish a decomposition theorem of D(μ).
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