On series expansions of hyperholomorphic Bq functions

In the previous article [11], B-q spaces of hyperholomorphic functions were studied and it was shown that these spaces form a scale of subspaces, all included in the hyperholomorphic Bloch space. Here, we study the problem if these inclusions within the scale and with respect to the Bloch space are strict. Main tool is the characterization of B-q functions by the coefficients of certain series expansions.