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Composition Operators in Bloch Spaces of Slice Hyperholomorphic Functions

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Abstract

In this paper we define Bloch-type spaces of slice hyperholomorphic functions in the unit ball \(\mathbb {B}.\) We study the invariance of these spaces with slice regular Möbius transformation and also give some simple characterizations for boundedness and compactness of composition operators on the slice regular Bloch-type spaces on the unit ball \(\mathbb {B}.\) We also estimate the essential norm of these operators.

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Acknowledgements

The authors are grateful to the referee for the valuable suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics, Central University of Jammu, Jammu, 180 011, India

    Sanjay Kumar, Khalid Manzoor & Pavinder Singh

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  1. Sanjay Kumar
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  2. Khalid Manzoor
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  3. Pavinder Singh
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Correspondence to Sanjay Kumar.

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Communicated by Vladislav Kravchenko

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Kumar, S., Manzoor, K. & Singh, P. Composition Operators in Bloch Spaces of Slice Hyperholomorphic Functions. Adv. Appl. Clifford Algebras 27, 1459–1477 (2017). https://doi.org/10.1007/s00006-016-0737-z

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  • DOI: https://doi.org/10.1007/s00006-016-0737-z

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