On hyperholomorphic Fω,Gα(p,q,s) spaces of quaternion valued functions

Abstract

The purpose of this paper is to define a new class of hyperholomorphic functions spaces, which will be called $F_{\omega ,G}^{\alpha }(p,q,s)$ type spaces. For this class, we characterize hyperholomorphic weighted $\alpha$-Bloch functions by functions belonging to $F_{\omega ,G}^{\alpha }(p,q,s)$ 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 $F_{\omega ,G}^{\alpha }(p,q,s)$ spaces of hyperholomorphic functions. Finally, we will give the relation between the hyperholomorphic ${\mathcal{B}}_{\omega ,0}^{\alpha }$ type spaces and the hyperholomorphic valued-functions space $F_{\omega ,G}^{\alpha }(p,q,s)$.