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On weighted Dirichlet spaces of monogenic functions in R 3
Author(s) -
Avetisyan Karen,
Gürlebeck Klaus
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5309
Subject(s) - mathematics , bounded function , ball (mathematics) , dirichlet distribution , pure mathematics , harmonic function , operator (biology) , quaternion , dirichlet problem , bounded operator , mathematical analysis , boundary value problem , geometry , biochemistry , chemistry , repressor , transcription factor , gene
In a recent paper of ours, we proved that a special “harmonic conjugation” operator is not bounded in weighted Bergman spacesL α 2of quaternion‐valued functions in the 3D ball. In the present paper, we prove that, in contrast to the Bergman spaces case, the same operator is bounded in weighted Dirichlet spacesD α 2of quaternion‐valued functions in the 3D ball. Furthermore, applying another approach for a construction of harmonic conjugates, we extend the result to weighted Dirichlet spacesD α pwith 1 < p < ∞ .