Complex Analysis and Operator Theory

, Volume 13, Issue 1, pp 45–59 | Cite as

On the Closures of Dirichlet Type Spaces in the Bloch Space

  • Guanlong BaoEmail author
  • Nihat Gökhan Göğüş


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.


The Bloch space Dirichlet type spaces Closure Interpolating Blaschke product 

Mathematics Subject Classification

30H30 30J10 46E15 



The authors thank the referee and the editor for providing useful suggestions. The work was done while G. Bao was at Sabanci University from 01 February 2016 to 31 January 2017. It is his pleasure to acknowledge the excellent working environment provided to him there.


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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Department of MathematicsShantou UniversityShantouChina
  2. 2.Faculty of Engineering and Natural SciencesSabanci UniversityTuzla, IstanbulTurkey

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