Characterizations of Dirichlet-type Spaces

2013/04/22 by Liu, Xiaosong, Chacón, Gerardo R., Lou, Zengjian
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 30D45 #Secondary 30D50

paper · doi:10.48550/arxiv.1304.5958

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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