  In this paper, we continue the development of a fundament of discrete
octonionic analysis that is associated to the discrete first order
Cauchy-Riemann operator acting on octonions. In particular, we establish a
discrete octonionic version of the Borel-Pompeiu formula and of Cauchy's
integral formula. The latter then is exploited to introduce a discrete
monogenic octonionic Cauchy transform. This tool in hand allows us to introduce
discrete octonionic Hardy spaces for upper and lower half-space together with
Plemelj projection formulae.

Complex Variables