On BQ spaces of hyperholomorphic functions and the Bloch space in R3

Recently a definition of B-q spaces of hyperholomorphic functions of three real variables has been presented by the same authors (see [15]). This definition allows to characterize the hypercomplex Bloch space equivalently by the integral norms of B-q. The aim of this paper is to describe a "wider" scale of B-q spaces of hyperholomorphic functions by using another weight function. A part of the scale still characterizes the Bloch space but the whole scale is not longer equivalent to the Bloch space. Besides, some important basic properties of these weighted B-q spaces are also considered.