Quaternionic $$F (p,q,s)$$ F ( p , q , s ) Function Spaces

Abstract

In this paper we develop the necessary tools to generalize the function spaces \(F(p,q,s)\) and \(F_0(p,q,s)\) introduced by Zhao in (Zhao, Ann Acad Sci Fenn Math Diss No 105, 1996) to the case of the monogenic functions defined in the unit ball of \(\mathbb {R}^3\). Obtaining at the same time the generalization of \({\mathcal {Q}}_p\) monogenic spaces presented in (Gurlebeck et al., On \(\mathbb {Q}_{p}-\)spaces of quaternion-valued functions, 1999) and \(B^{q,p}\) monogenic spaces in (El-Sayed Ahmed et al., Complex Var Elliptic Equ 51(2):119–136, 2006).