TY - JOUR
T1 - Bloch, Besov and Dirichlet Spaces of Slice Hyperholomorphic Functions
AU - Castillo Villalba, C. Marco Polo
AU - Colombo, Fabrizio
AU - Gantner, Jonathan
AU - González-Cervantes, J. Oscar
N1 - Publisher Copyright:
© 2014, Springer Basel.
PY - 2015/2
Y1 - 2015/2
N2 - 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.
AB - 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.
KW - Besov spaces
KW - Bloch spaces
KW - Dirichlet spaces
KW - Slice hyperholomorphic functions
UR - http://www.scopus.com/inward/record.url?scp=84939888635&partnerID=8YFLogxK
U2 - 10.1007/s11785-014-0380-4
DO - 10.1007/s11785-014-0380-4
M3 - Artículo
SN - 1661-8254
VL - 9
SP - 479
EP - 517
JO - Complex Analysis and Operator Theory
JF - Complex Analysis and Operator Theory
IS - 2
ER -