Abstract
Some characterizations of the so-called Dirichlet-type spaces \(D(\mu )\) are given. First we characterize \(D(\mu )\) by means of the derivative free integral and of the mean oscillation in the Bergman metric. We then obtain a characterization for \(D(\mu )\) that makes use of high-order derivative. Finally, as the main result of this article, we establish a decomposition theorem of \(D(\mu )\).
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Communicated by Vladimir Bolotnikov.
This work was supported by NNSF of China (Grant No. 11171203, 11201280), NSF of Guangdong Province (Grant No. 10151503101000025, S2011010004511, S2011040004131), and was partially supported by Pontificia Universidad Javeriana (Research Proyect No. 5568).
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Liu, X., Chacón, G.R. & Lou, Z. Characterizations of the Dirichlet-Type Space. Complex Anal. Oper. Theory 9, 1269–1286 (2015). https://doi.org/10.1007/s11785-014-0404-0
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DOI: https://doi.org/10.1007/s11785-014-0404-0