INTEGRAL NORMS FOR HYPERHOLOMORPHIC BLOCH-FUNCTIONS IN THE UNIT BALL OF ℝ³

We extend the concept of B^q spaces from the one-dimensional complex function theory to spaces of hyperholomorphic quaternion-valued functions of three real variables. Moreover, we will study some properties of these spaces and prove a characterization of hyperholomorphic Bloch functions in the unit ball of ℝ³ by integral norms.