Korean J. Math.  Vol 26, No 1 (2018)  pp.87-101
DOI: http://dx.doi.org/10.11568/kjm.2018.26.1.87

On hyperholomorphic $F^{\alpha}_{\omega,G}(p,q,s)$ spaces of quaternion valued functions

Alaa Kamal, Taha Ibrahim Yassen


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 $F^{\alpha}_{\omega,G}(p,q,s)$.


Quaternionic analysis, $F^{\alpha}_{\omega,G}(p,q,s)$ spaces, hyperholomorphic functions, Clifford analysis

Subject classification

$30G35$, $46E15$


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