Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON HYPERHOLOMORPHIC Fαω,G(p, q, s) SPACES OF QUATERNION VALUED FUNCTIONS

  • Kamal, Alaa (Department of Mathematics, Qassim University College of Sciences and Arts in Muthnib) ;
  • Yassen, Taha Ibrahim (Department of Mathematics faculty of Sciences Port Said University)
  • Received : 2017.06.11
  • Accepted : 2018.03.20
  • Published : 2018.03.30
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Abstract

The purpose of this paper is to define a new class of hyperholomorphic functions spaces, which will be called $F^{\alpha}_{{\omega},G}$(p, q, s) type spaces. For this class, we characterize hyperholomorphic weighted ${\alpha}$-Bloch functions by functions belonging to $F^{\alpha}_{{\omega},G}$(p, q, s) spaces under some mild conditions. Moreover, we give some essential properties for the extended weighted little ${\alpha}$-Bloch spaces. Also, we give the characterization for the hyperholomorphic weighted Bloch space by the integral norms of $F^{\alpha}_{{\omega},G}$(p, q, s) spaces of hyperholomorphic functions. Finally, we will give the relation between the hyperholomorphic ${\mathcal{B}}^{\alpha}_{{\omega},0}$ type spaces and the hyperholomorphic valued-functions space $F^{\alpha}_{{\omega},G}$(p, q, s).

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References

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