On weighted Dirichlet spaces of monogenic functions in    R  3 | Zendy

Avetisyan Karen | Zendy; Gürlebeck Klaus | Zendy

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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 < ∞ .

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