Characterizations of Dirichlet-type Spaces
Complex Variables
2013-04-23 v1 Functional Analysis
Abstract
We give three characterizations of the Dirichlet-type spaces . First we characterize 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 in terms of higher order derivatives. Also, a decomposition theorem for is established.
Cite
@article{arxiv.1304.5958,
title = {Characterizations of Dirichlet-type Spaces},
author = {Xiaosong Liu and Gerardo R. Chacón and Zengjian Lou},
journal= {arXiv preprint arXiv:1304.5958},
year = {2013}
}