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