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BMO‐ and VMO‐spaces of slice hyperholomorphic functions
Author(s) -
Gantner Jonathan,
GonzálezCervantes J. Oscar,
Janssens Tim
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600379
Subject(s) - mathematics , pure mathematics , unit sphere , geodesic , hardy space , space (punctuation) , relation (database) , algebra over a field , operator theory , duality (order theory) , characterization (materials science) , mathematical analysis , computer science , materials science , nanotechnology , operating system , database
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 spaceH 1 ( D ) . 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.