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arXiv · 1304.5958

Characterizations of Dirichlet-type Spaces

Xiaosong Liu·Gerardo R. Chacón·Zengjian Lou
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Abstract

We give three characterizations of the Dirichlet-type spaces $D(μ)$. First we characterize $D(μ)$ in terms of a double integral and in terms of the mean oscillation in the Bergman metric, none of them involve the use of derivatives. Next, we obtain another characterization for $D(μ)$ in terms of higher order derivatives. Also, a decomposition theorem for $D(μ)$ is established.

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Xiaosong Liu, Gerardo R. Chacón, Zengjian Lou. 2013-04-22. Characterizations of Dirichlet-type Spaces. https://arxiv.org/abs/1304.5958

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