On the closures of Dirichlet type spaces in the Bloch space
Bao, Guanlong and Göğüş, Nihat Gökhan (2017) On the closures of Dirichlet type spaces in the Bloch space. Complex Analysis and Operator Theory . ISSN 1661-8254 (Print) 1661-8262 (Online) Published Online First http://dx.doi.org/10.1007/s11785-017-0676-2
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Official URL: http://dx.doi.org/10.1007/s11785-017-0676-2
In this paper, via high order derivatives and via embedding derivatives of Bloch type functions into Lebesgue spaces, we characterize the closures of Dirichlet type spaces in the Bloch space. We obtain the inclusion relation between the closures and the little Bloch space. We consider the separability of the closures as Banach spaces. A criterion for an interpolating Blaschke product to be in the closures is given. We also consider the relation between the closures and the space of bounded analytic functions.
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