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In this paper we develop the necessary tools to generalize the function spaces F(p; q; s)and F0(p; q; s)introduced by Zhao in [Zha] to the case of the monogenic functions defined in the unit ball of R3.Obtaining at the same time the generalization of Qp monogenic spaces presented in [GuKaShTo] and Bq,p monogenic spaces in [ElGuReTo].