Volume 290, Issue 14-15 pp. 2259-2279
ORIGINAL PAPER

BMO- and VMO-spaces of slice hyperholomorphic functions

Jonathan Gantner

Corresponding Author

Jonathan Gantner

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

Correspondence

Jonathan Gantner, Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133 Milano, Italy.

Email: [email protected]

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J. Oscar González-Cervantes

J. Oscar González-Cervantes

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

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Tim Janssens

Tim Janssens

University of Antwerp, Department of Mathematics, Middelheimlaan, 1, 2020 Antwerp, Belgium

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First published: 18 April 2017
Citations: 10

Abstract

In this paper we continue the study of important Banach spaces of slice hyperholomorphic functions on the quaternionic unit ball by investigating the BMO- and VMO-spaces of slice hyperholomorphic functions. We discuss in particular conformal invariance and a refined characterization of these spaces in terms of Carleson measures. Finally we show the relations with the Bloch and Dirichlet space and the duality relation with the Hardy space urn:x-wiley:0025584X:media:mana201600379:mana201600379-math-0001. The importance of these spaces in the classical theory is well known. It is therefore worthwhile to study their slice hyperholomorphic counterparts, in particular because slice hyperholomorphic functions were found to have several applications in operator theory and Schur analysis.

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