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Functions of several octonion variables are investigated and integralrepresentation theorems for them are proved. With the help of them solutions ofthe ${\tilde {\partial}}$-equations are studied. More generally functions ofseveral Cayley-Dickson variables are considered. Integral formulas of theMartinelli-Bochner, Leray, Koppelman type used in complex analysis here areproved in the new generalized form for functions of Cayley-Dickson variablesinstead of complex. Moreover, analogs of Stein manifolds over Cayley-Dicksongraded algebras are defined and investigated.

Functions of several Cayley-Dickson variables and manifolds over them