TY - JOUR
T1 - Further properties of the Bergman spaces of slice regular functions
AU - Colombo, Fabrizio
AU - González-Cervantes, J. Oscar
AU - Sabadini, Irene
N1 - Publisher Copyright:
© 2015 by Walter de Gruyter Berlin/Boston.
PY - 2015/10/1
Y1 - 2015/10/1
N2 - We continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind. In this paperwe mainly consider the Bergman theory of the second kind, by providing an explicit description of the Bergman kernel in the case of the unit ball and of the half space. In the case of the unit ball, we study the Bergman-Sce transform. We also show that the two Bergman theories can be compared only if suitableweights are taken into account. Finally,we use the Schwarz reflection principle to relate the Bergman kernel with its values on a complex half plane.
AB - We continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind. In this paperwe mainly consider the Bergman theory of the second kind, by providing an explicit description of the Bergman kernel in the case of the unit ball and of the half space. In the case of the unit ball, we study the Bergman-Sce transform. We also show that the two Bergman theories can be compared only if suitableweights are taken into account. Finally,we use the Schwarz reflection principle to relate the Bergman kernel with its values on a complex half plane.
KW - Bergman kernel
KW - Bergman-Fueter transform
KW - Schwarz reflection principle
KW - Slice regular functions
UR - http://www.scopus.com/inward/record.url?scp=84945186026&partnerID=8YFLogxK
U2 - 10.1515/advgeom-2015-0022
DO - 10.1515/advgeom-2015-0022
M3 - Artículo
AN - SCOPUS:84945186026
SN - 1615-715X
VL - 15
SP - 469
EP - 484
JO - Advances in Geometry
JF - Advances in Geometry
IS - 4
ER -