Bloch, Besov and Dirichlet Spaces of Slice Hyperholomorphic Functions

C. Marco Polo Castillo Villalba, Fabrizio Colombo, Jonathan Gantner, J. Oscar González-Cervantes

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

© 2014, Springer Basel. 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.
Original languageAmerican English
Pages (from-to)479-517
Number of pages427
JournalComplex Analysis and Operator Theory
DOIs
StatePublished - 1 Jan 2015

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