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Bloch, Besov and Dirichlet Spaces of Slice Hyperholomorphic Functions

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Abstract

In this paper we begin the study of some important Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and we also consider the Dirichlet space, which is a Hilbert space. The importance of these spaces is well known, and thus their study in the framework of slice hyperholomorphic functions is relevant, especially in view of the fact that this class of functions has recently found several applications in operator theory and in Schur analysis. We also discuss the property of invariance of these function spaces with respect to Möbius maps by using a suitable notion of composition.

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Authors and Affiliations

  1. Instituto de Matematicas, Cuidad Universitaria, Unidad de Posgrado, C.P. 04510 , Mexico, D.F., Mexico

    C. Marco Polo Castillo Villalba

  2. Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, 20133 , Milan, Italy

    Fabrizio Colombo

  3. Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 , Vienna, Austria

    Jonathan Gantner

  4. Departamento de Matemáticas, E.S.F.M. del I.P.N., 07338 , Mexico, D.F., Mexico

    J. Oscar González-Cervantes

Authors
  1. C. Marco Polo Castillo Villalba
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  2. Fabrizio Colombo
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  3. Jonathan Gantner
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  4. J. Oscar González-Cervantes
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Correspondence to Fabrizio Colombo.

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Communicated by Daniel Aron Alpay.

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Castillo Villalba, C.M.P., Colombo, F., Gantner, J. et al. Bloch, Besov and Dirichlet Spaces of Slice Hyperholomorphic Functions. Complex Anal. Oper. Theory 9, 479–517 (2015). https://doi.org/10.1007/s11785-014-0380-4

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  • DOI: https://doi.org/10.1007/s11785-014-0380-4

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