Hp-spaces of monogenic functions

The classical theory of HP spaces (see e.g. [1] and [2]) combines the notions of holomorphy and boundary behaviour in Lp-sense. In this paper we introduce the concept of HP space in the unit ball of the Euclidean Space of arbitrary dimension, by considering the so called monogenic functions, which are a natural generalization to higher dimension of the holomorphic functions of one complex variable. Several possible definitions of the HP space of monogenic functions in the unit ball of Rm are given. The aim is to establish the equivalence of those definitions, providing in this way the basis properties of HP functions considered.