On the Closures of Dirichlet Type Spaces in the Bloch Space

Article

Abstract

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.

Keywords

The Bloch space Dirichlet type spaces Closure Interpolating Blaschke product 

Mathematics Subject Classification

30H30 30J10 46E15 

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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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