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Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball

Abstract

For, let and denote, respectively, the-Bloch and holomorphic-Lipschitz spaces of the open unit ball in. It is known that and are equal as sets when. We prove that these spaces are additionally norm-equivalent, thus extending known results for and the polydisk. As an application, we generalize work by Madigan on the disk by investigating boundedness of the composition operator from to.

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Correspondence to Dana D. Clahane.

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Clahane, D.D., Stević, S. Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball. J Inequal Appl 2006, 61018 (2006). https://doi.org/10.1155/JIA/2006/61018

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Keywords

  • Unit Ball
  • Open Unit
  • Composition Operator
  • Lipschitz Space
  • Open Unit Ball
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