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

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

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Published: Mar 20, 2018
Keywords:
Quaternionic analysis, $F^{\alpha}_{\omega, G}(p, q, s)$ spaces, hyperholomorphic functions, Clifford analysis
Mathematics Subject Classification:
$30G35$, $46E15$

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Alaa Kamal
Department of Mathematics, Qassim University College of Sciences and Arts in Muthnib Qassim, KSA.
Taha Ibrahim Yassen
Department of Mathematics faculty of Sciences Port Said University Port Said, Egypt

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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