Computational Methods and Function Theory 9 (2009), No. 2, 593--608
Copyright Heldermann Verlag 2009
Karen Avetisyan
avetkaren@ysu.am , Yerevan State University, Faculty of Physics, Alex Manoogian St. 1, Yerevan, 375025, Armenia.
Klaus Gürlebeck
klaus.guerlebeck@uni-weimar.de , Bauhaus-Universität Weimar, Institut für Mathematik/Physik, Coudray-Str. 13 B, 99423 Weimar, Germany.
Wolfgang Spr&ossig
sproessig@math.tu-freiberg.de , Technische Universität Bergakademie Freiberg, Institut für Angewandte Analysis, 09596 Freiberg, Germany.
In this paper we study the harmonic conjugation problem in weighted Bergman spaces of quaternion-valued functions on the unit ball. For a scalar-valued harmonic function belonging to a Bergman space, harmonic conjugates in the same Bergman space are found.
Keywords: Quaternion, monogenic function, harmonic Bergman spaces.
MSC 2000: 30G35, 31B05.
[FullText-pdf (308 K)] [FullText-ps (512 K)]